| | |
- graphs.BipartiteGraph(graphs.Graph)
-
- InterGroupPairing
-
- BestCopelandInterGroupMatching
- FairestGaleShapleyMatching
- FairestInterGroupPairing
- FairnessEnhancedInterGroupMatching
- graphs.Graph(builtins.object)
-
- IntraGroupPairing
-
- BestCopelandIntraGroupMatching
- FairestIntraGroupPairing
- FairnessEnhancedIntraGroupMatching
class BestCopelandInterGroupMatching(InterGroupPairing) |
| |
BestCopelandInterGroupMatching(vpA, vpB, Comments=False, Debug=False)
The class computes the individual Copeland ranking scores and
constructs a best determined perfect intergroup matching
with a ranked pairs rule
*Parameters*:
* *vpA* : any VotingProfile instance
* *vpB* : reciprocal VotingProfile instance
See the :ref:`tutorial on computing fair intergroup pairings <Fair-InterGroup-Pairings-label>`.
|
| |
- Method resolution order:
- BestCopelandInterGroupMatching
- InterGroupPairing
- graphs.BipartiteGraph
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self, vpA, vpB, Comments=False, Debug=False)
- Abstract class entry
Methods inherited from InterGroupPairing:
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, vpA, a, b)
- Replacement for the linear voting profiles information
when searching for promising swapping candidates
- computeGaleShapleyMatching(self, Reverse=False)
- Documentation:
https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
When *Reverse==False*, group *A* is proposing.
Otherwise, group *B* is proposing
- computeIndividualCorrelations(self, matching, Debug=False)
- Individual correlations for groups A and B
returns a tuple called fitness with following content
fitness=(matching,avgCorr,stdCorr,avgCorr-stdCorr,
groupAScores,groupBScores,
abs(avgCorrA-avgCorrB))
- computePermutation(self, matching)
- Renders the matching's permutation of *A* and *B* indexes.
.. note:: The prefix of group *A* voters must preceed the prefix of the group *B* voters in alphabetic order
- computePermutationGraph(self, matching)
- Renders the permutation graph of the matching
- enhanceMatchingGeneralFairness(self, matching, maxIterations=10, Comments=False, Debug=False)
- Enahance fairness of a given matching using any reciprocal voting profiles
- enhanceMatchingLVFairness(self, matching, Reversed=False, maxIterations=10, Comments=False, Debug=False)
- Enhance fairness of given matching by using reciprocal linear voting profiles
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- isStableMatching(self, matching, Comments=True, Debug=False)
- Test for the existance of matching instabilities.
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
- showCopelandRankingScores(self)
- Print the individual Copeland ranking scores
- showMatchingFairness(self, matching=None, WithGroupCorrelations=True, WithIndividualCorrelations=True)
- showPairing(self, matching=None)
Methods inherited from graphs.BipartiteGraph:
- computeBestDeterminedMaximalMatching(self, Comments=True, Debug=True)
- Using the ranked pairs rule for assembling a best determined maximal matching
- exportGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', edgeColor='blue', bgcolor='cornsilk', lineWidth=1, Debug=True)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class BestCopelandIntraGroupMatching(IntraGroupPairing) |
| |
BestCopelandIntraGroupMatching(vpA, Comments=False, Debug=False)
The class computes the individual Copeland ranking scores and
construct the best determined perfect matching with a ranked pairs rule
from the reciprocal Copeland ranking scores graph
*Parameters*:
* *vpA* : intragroup *VotingProfile* instance
See the :ref:`tutorial on computing fair intergroup pairings <Fair-InterGroup-Pairings-label>`.
|
| |
- Method resolution order:
- BestCopelandIntraGroupMatching
- IntraGroupPairing
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self, vpA, Comments=False, Debug=False)
- Constructor for Graph objects.
Methods inherited from IntraGroupPairing:
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, a, b)
- Computes fitness of swapping candidates
- computeIndividualCorrelations(self, matching=None, Debug=False)
- Individual correlations for intragroup pairing solution
returns a tuple called fitness with following content
avgCorr,stdCorr, groupScores
- enhanceMatchingFairness(self, matching, Comments=False, Debug=False)
- Heuristic for fairness enhancing of given matching
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=2)
- Exports GraphViz dot file for pairing graph drawing filtering.
- showMatchingFairness(self, matching=None, WithIndividualCorrelations=True)
- Shows the intragroup faines of a given matching.
When *matching is None* the fairest matching of the class is used
- showPairing(self, matching=None)
- shows the intragroup pairing solution when *matching is None*
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computePermutation(self, seq1=None, seq2=None, Comments=True)
- Tests whether the graph instance *self* is a permutation graph
and renders, in case the test is positive,
the corresponding permutation.
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', WithSpanningTree=False, WithVertexColoring=False, matching=None, layout=None, arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for graph drawing filtering.
Example:
>>> g = Graph(numberOfVertices=5,edgeProbability=0.3)
>>> g.exportGraphViz('randomGraph')
.. image:: randomGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class FairestGaleShapleyMatching(InterGroupPairing) |
| |
FairestGaleShapleyMatching(lvA, lvB, Comments=False)
The class computes both Gale-Shapley matchings -- group A proposes and group B proposes--
and renders the fairest of both.
*Parameters*:
* *lvA* : LinearVotingProfile instance
* *lvB* : reciprocal LinearVotingProfile
See the :ref:`tutorial on computing fair intergroup pairings <Fair-InterGroup-Pairings-label>`.
|
| |
- Method resolution order:
- FairestGaleShapleyMatching
- InterGroupPairing
- graphs.BipartiteGraph
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self, lvA, lvB, Comments=False)
- Abstract class entry
Methods inherited from InterGroupPairing:
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, vpA, a, b)
- Replacement for the linear voting profiles information
when searching for promising swapping candidates
- computeGaleShapleyMatching(self, Reverse=False)
- Documentation:
https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
When *Reverse==False*, group *A* is proposing.
Otherwise, group *B* is proposing
- computeIndividualCorrelations(self, matching, Debug=False)
- Individual correlations for groups A and B
returns a tuple called fitness with following content
fitness=(matching,avgCorr,stdCorr,avgCorr-stdCorr,
groupAScores,groupBScores,
abs(avgCorrA-avgCorrB))
- computePermutation(self, matching)
- Renders the matching's permutation of *A* and *B* indexes.
.. note:: The prefix of group *A* voters must preceed the prefix of the group *B* voters in alphabetic order
- computePermutationGraph(self, matching)
- Renders the permutation graph of the matching
- enhanceMatchingGeneralFairness(self, matching, maxIterations=10, Comments=False, Debug=False)
- Enahance fairness of a given matching using any reciprocal voting profiles
- enhanceMatchingLVFairness(self, matching, Reversed=False, maxIterations=10, Comments=False, Debug=False)
- Enhance fairness of given matching by using reciprocal linear voting profiles
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- isStableMatching(self, matching, Comments=True, Debug=False)
- Test for the existance of matching instabilities.
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
- showCopelandRankingScores(self)
- Print the individual Copeland ranking scores
- showMatchingFairness(self, matching=None, WithGroupCorrelations=True, WithIndividualCorrelations=True)
- showPairing(self, matching=None)
Methods inherited from graphs.BipartiteGraph:
- computeBestDeterminedMaximalMatching(self, Comments=True, Debug=True)
- Using the ranked pairs rule for assembling a best determined maximal matching
- exportGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', edgeColor='blue', bgcolor='cornsilk', lineWidth=1, Debug=True)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class FairestInterGroupPairing(InterGroupPairing) |
| |
FairestInterGroupPairing(vpA, vpB, orderLimit=6, StableMatchings=False, Comments=False, Debug=False)
The class computes the fitness scores of the complete set of maximal matchings between
two groups *A* and *B* of persons of equal number *k* and delivers, based on these fitness scores, a fairest pairing of the persons of both groups.
*Parameters*:
* *vpA* : any type of VotingProfile instance
* *vpB* : reciprocal VotingProfile instance
* *oderLimit* : preventing a potential CPU memory or time overflow
* *StableMatchings* : False (default) / True limits to only stable matchings
See the :ref:`tutorial on computing fair intergroup pairings <Fair-InterGroup-Pairings-label>`.
|
| |
- Method resolution order:
- FairestInterGroupPairing
- InterGroupPairing
- graphs.BipartiteGraph
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self, vpA, vpB, orderLimit=6, StableMatchings=False, Comments=False, Debug=False)
- Abstract class entry
- computeMatchingFairnessIndex(self, matching, Comments=False)
- Renders the index position of the given matching in the
fairness ranked self.pairings list.
- showFairestPairing(self, rank=1, WithIndividualCorrelations=False)
- Setting the *rank* parameter to a value > 1,
gives access to lesser fitting pairings.
The *WithIndividualCorrelations* flag shows the correlations with
the individual pairing preferences.
Methods inherited from InterGroupPairing:
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, vpA, a, b)
- Replacement for the linear voting profiles information
when searching for promising swapping candidates
- computeGaleShapleyMatching(self, Reverse=False)
- Documentation:
https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
When *Reverse==False*, group *A* is proposing.
Otherwise, group *B* is proposing
- computeIndividualCorrelations(self, matching, Debug=False)
- Individual correlations for groups A and B
returns a tuple called fitness with following content
fitness=(matching,avgCorr,stdCorr,avgCorr-stdCorr,
groupAScores,groupBScores,
abs(avgCorrA-avgCorrB))
- computePermutation(self, matching)
- Renders the matching's permutation of *A* and *B* indexes.
.. note:: The prefix of group *A* voters must preceed the prefix of the group *B* voters in alphabetic order
- computePermutationGraph(self, matching)
- Renders the permutation graph of the matching
- enhanceMatchingGeneralFairness(self, matching, maxIterations=10, Comments=False, Debug=False)
- Enahance fairness of a given matching using any reciprocal voting profiles
- enhanceMatchingLVFairness(self, matching, Reversed=False, maxIterations=10, Comments=False, Debug=False)
- Enhance fairness of given matching by using reciprocal linear voting profiles
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- isStableMatching(self, matching, Comments=True, Debug=False)
- Test for the existance of matching instabilities.
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
- showCopelandRankingScores(self)
- Print the individual Copeland ranking scores
- showMatchingFairness(self, matching=None, WithGroupCorrelations=True, WithIndividualCorrelations=True)
- showPairing(self, matching=None)
Methods inherited from graphs.BipartiteGraph:
- computeBestDeterminedMaximalMatching(self, Comments=True, Debug=True)
- Using the ranked pairs rule for assembling a best determined maximal matching
- exportGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', edgeColor='blue', bgcolor='cornsilk', lineWidth=1, Debug=True)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class FairestIntraGroupPairing(IntraGroupPairing) |
| |
FairestIntraGroupPairing(vp, orderLimit=6, Comments=False, Debug=False)
The class computes average ordinal correlations for the complete set of maximal IntraGroup matchings
of an een-sized set of persons and delivers, based on these correlations scores,
a fairest possible pairing of the persons
*Parameters*:
* *vpA* : any type of VotingProfile instance
* *oderLimit* : preventing a potential CPU memory or time overflow
See the :ref:`tutorial on computing fair intragroup pairings <Fair-IntraGroup-Pairings-label>`.
|
| |
- Method resolution order:
- FairestIntraGroupPairing
- IntraGroupPairing
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self, vp, orderLimit=6, Comments=False, Debug=False)
- Constructor for Graph objects.
- computeMatchingFairnessIndex(self, matching, Comments=False)
- Renders the index position of the given matching in the
fairness ranked self.pairings list.
Methods inherited from IntraGroupPairing:
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, a, b)
- Computes fitness of swapping candidates
- computeIndividualCorrelations(self, matching=None, Debug=False)
- Individual correlations for intragroup pairing solution
returns a tuple called fitness with following content
avgCorr,stdCorr, groupScores
- enhanceMatchingFairness(self, matching, Comments=False, Debug=False)
- Heuristic for fairness enhancing of given matching
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=2)
- Exports GraphViz dot file for pairing graph drawing filtering.
- showMatchingFairness(self, matching=None, WithIndividualCorrelations=True)
- Shows the intragroup faines of a given matching.
When *matching is None* the fairest matching of the class is used
- showPairing(self, matching=None)
- shows the intragroup pairing solution when *matching is None*
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computePermutation(self, seq1=None, seq2=None, Comments=True)
- Tests whether the graph instance *self* is a permutation graph
and renders, in case the test is positive,
the corresponding permutation.
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', WithSpanningTree=False, WithVertexColoring=False, matching=None, layout=None, arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for graph drawing filtering.
Example:
>>> g = Graph(numberOfVertices=5,edgeProbability=0.3)
>>> g.exportGraphViz('randomGraph')
.. image:: randomGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class FairnessEnhancedInterGroupMatching(InterGroupPairing) |
| |
FairnessEnhancedInterGroupMatching(vpA, vpB, initialMatching=None, seed=None, maxIterations=None, Comments=False, Debug=False)
The class enhances the fairness of a given matching.
*Parameters*:
* *vpA* : any VotingProfile instance
* *vpB* : reciprocal VotingProfile instance
* *initialMatching* : a given perfect matching
if *None* a matching is being previously constructed
elif 'bestCopeland' a best Copeland intergroup matching is used,
elif 'Random' a shuffled version of the bi is matched to the ai,
* The *seed* parameter is used for allowing to repete the same experiment
See the :ref:`tutorial on computing fair intergroup pairings <Fair-InterGroup-Pairings-label>`.
|
| |
- Method resolution order:
- FairnessEnhancedInterGroupMatching
- InterGroupPairing
- graphs.BipartiteGraph
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self, vpA, vpB, initialMatching=None, seed=None, maxIterations=None, Comments=False, Debug=False)
- Abstract class entry
Methods inherited from InterGroupPairing:
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, vpA, a, b)
- Replacement for the linear voting profiles information
when searching for promising swapping candidates
- computeGaleShapleyMatching(self, Reverse=False)
- Documentation:
https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
When *Reverse==False*, group *A* is proposing.
Otherwise, group *B* is proposing
- computeIndividualCorrelations(self, matching, Debug=False)
- Individual correlations for groups A and B
returns a tuple called fitness with following content
fitness=(matching,avgCorr,stdCorr,avgCorr-stdCorr,
groupAScores,groupBScores,
abs(avgCorrA-avgCorrB))
- computePermutation(self, matching)
- Renders the matching's permutation of *A* and *B* indexes.
.. note:: The prefix of group *A* voters must preceed the prefix of the group *B* voters in alphabetic order
- computePermutationGraph(self, matching)
- Renders the permutation graph of the matching
- enhanceMatchingGeneralFairness(self, matching, maxIterations=10, Comments=False, Debug=False)
- Enahance fairness of a given matching using any reciprocal voting profiles
- enhanceMatchingLVFairness(self, matching, Reversed=False, maxIterations=10, Comments=False, Debug=False)
- Enhance fairness of given matching by using reciprocal linear voting profiles
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- isStableMatching(self, matching, Comments=True, Debug=False)
- Test for the existance of matching instabilities.
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
- showCopelandRankingScores(self)
- Print the individual Copeland ranking scores
- showMatchingFairness(self, matching=None, WithGroupCorrelations=True, WithIndividualCorrelations=True)
- showPairing(self, matching=None)
Methods inherited from graphs.BipartiteGraph:
- computeBestDeterminedMaximalMatching(self, Comments=True, Debug=True)
- Using the ranked pairs rule for assembling a best determined maximal matching
- exportGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', edgeColor='blue', bgcolor='cornsilk', lineWidth=1, Debug=True)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class FairnessEnhancedIntraGroupMatching(IntraGroupPairing) |
| |
FairnessEnhancedIntraGroupMatching(intraVp=None, maxIterations=None, initialMatching=None, _nbrOfSwappingRetrials=None, seed=None, Comments=True, Debug=False)
Solver for computing fair IntraGroup pairings using a similar hill climbing heuristic as the
one for the intergroup pairing problem. The enhancing is guided by Copeland ranking scores.
*Parameters*:
* *intraVp* : a IntraGroup voting profile instance with *2k* voters where the *2k-1* candidates of
each person are the other persons
* *initialMatching* : the matching from which the fairness enhancing algorithm is starting
If *None*, a right --[pi,pi+1] for i = 1..2k-1 step 3-- and a left --[pi,p-i] for i = 1..k-- initial matching will be used
elif 'random' a random maximal matching will be used with given *seed*
elif 'bestCopeland' the best Copeland matching will be used as initial matching
See the :ref:`tutorial on computing fair intragroup pairings <Fair-IntraGroup-Pairings-label>`.
|
| |
- Method resolution order:
- FairnessEnhancedIntraGroupMatching
- IntraGroupPairing
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self, intraVp=None, maxIterations=None, initialMatching=None, _nbrOfSwappingRetrials=None, seed=None, Comments=True, Debug=False)
- Constructor for Graph objects.
Methods inherited from IntraGroupPairing:
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, a, b)
- Computes fitness of swapping candidates
- computeIndividualCorrelations(self, matching=None, Debug=False)
- Individual correlations for intragroup pairing solution
returns a tuple called fitness with following content
avgCorr,stdCorr, groupScores
- enhanceMatchingFairness(self, matching, Comments=False, Debug=False)
- Heuristic for fairness enhancing of given matching
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=2)
- Exports GraphViz dot file for pairing graph drawing filtering.
- showMatchingFairness(self, matching=None, WithIndividualCorrelations=True)
- Shows the intragroup faines of a given matching.
When *matching is None* the fairest matching of the class is used
- showPairing(self, matching=None)
- shows the intragroup pairing solution when *matching is None*
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computePermutation(self, seq1=None, seq2=None, Comments=True)
- Tests whether the graph instance *self* is a permutation graph
and renders, in case the test is positive,
the corresponding permutation.
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', WithSpanningTree=False, WithVertexColoring=False, matching=None, layout=None, arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for graph drawing filtering.
Example:
>>> g = Graph(numberOfVertices=5,edgeProbability=0.3)
>>> g.exportGraphViz('randomGraph')
.. image:: randomGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class InterGroupPairing(graphs.BipartiteGraph) |
| |
Abstract root class with private and public methods for intergroup pairing graphs
|
| |
- Method resolution order:
- InterGroupPairing
- graphs.BipartiteGraph
- graphs.Graph
- builtins.object
Methods defined here:
- __init__(self)
- Abstract class entry
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, vpA, a, b)
- Replacement for the linear voting profiles information
when searching for promising swapping candidates
- computeGaleShapleyMatching(self, Reverse=False)
- Documentation:
https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
When *Reverse==False*, group *A* is proposing.
Otherwise, group *B* is proposing
- computeIndividualCorrelations(self, matching, Debug=False)
- Individual correlations for groups A and B
returns a tuple called fitness with following content
fitness=(matching,avgCorr,stdCorr,avgCorr-stdCorr,
groupAScores,groupBScores,
abs(avgCorrA-avgCorrB))
- computePermutation(self, matching)
- Renders the matching's permutation of *A* and *B* indexes.
.. note:: The prefix of group *A* voters must preceed the prefix of the group *B* voters in alphabetic order
- computePermutationGraph(self, matching)
- Renders the permutation graph of the matching
- enhanceMatchingGeneralFairness(self, matching, maxIterations=10, Comments=False, Debug=False)
- Enahance fairness of a given matching using any reciprocal voting profiles
- enhanceMatchingLVFairness(self, matching, Reversed=False, maxIterations=10, Comments=False, Debug=False)
- Enhance fairness of given matching by using reciprocal linear voting profiles
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- isStableMatching(self, matching, Comments=True, Debug=False)
- Test for the existance of matching instabilities.
Our implementation is inspired by
https://johnlekberg.com/blog/2020-08-22-stable-matching.html
- showCopelandRankingScores(self)
- Print the individual Copeland ranking scores
- showMatchingFairness(self, matching=None, WithGroupCorrelations=True, WithIndividualCorrelations=True)
- showPairing(self, matching=None)
Methods inherited from graphs.BipartiteGraph:
- computeBestDeterminedMaximalMatching(self, Comments=True, Debug=True)
- Using the ranked pairs rule for assembling a best determined maximal matching
- exportGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', edgeColor='blue', bgcolor='cornsilk', lineWidth=1, Debug=True)
- Exports GraphViz dot file for bipartite graph drawing filtering.
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class IntraGroupPairing(graphs.Graph) |
| |
Abstract root class for IntraGroup pairing solutions
|
| |
- Method resolution order:
- IntraGroupPairing
- graphs.Graph
- builtins.object
Methods defined here:
- __init__()
- Constructor for Graph objects.
- __repr__(self)
- Default description for FairPairing instances.
- computeCopelandScore(self, a, b)
- Computes fitness of swapping candidates
- computeIndividualCorrelations(self, matching=None, Debug=False)
- Individual correlations for intragroup pairing solution
returns a tuple called fitness with following content
avgCorr,stdCorr, groupScores
- enhanceMatchingFairness(self, matching, Comments=False, Debug=False)
- Heuristic for fairness enhancing of given matching
- exportPairingGraphViz(self, fileName=None, Comments=True, graphType='png', graphSize='7,7', matching=None, edgeColor='blue', bgcolor='cornsilk', lineWidth=2)
- Exports GraphViz dot file for pairing graph drawing filtering.
- showMatchingFairness(self, matching=None, WithIndividualCorrelations=True)
- Shows the intragroup faines of a given matching.
When *matching is None* the fairest matching of the class is used
- showPairing(self, matching=None)
- shows the intragroup pairing solution when *matching is None*
Methods inherited from graphs.Graph:
- __neg__(self)
- Make the negation operator -self available for Graph instances.
Returns a DualGraph instance of self.
- breadthFirstSearch(self, s, alphabeticOrder=True, Warnings=True, Debug=False)
- Breadth first search through a graph in lexicographical order
of the vertex keys.
Renders a list of vertice keys in
increasing distance from the origin *s*. Ties in the distances
are resolved by alphabetic ordering of the vertice keys.
A warning is issued when the graph is not connected and the resulting
search does not cover the whole set of graph vertices.
Source: Cormen, Leiserson, Rivest & Stein, *Introduction to Algorithms* 2d Ed., MIT Press 2001.
- computeChordlessCycles(self, Cycle3=False, Comments=False, Debug=False)
- Renders the set of all chordless cycles observed in a Graph
intance. Inspired from Dias, Castonguay, Longo & Jradi,
Algorithmica 2015.
.. note::
By default, a chordless cycle must have at least length 4.If the Cycle3 flag is set to True,
the cyclicly closed triplets will be inserted as 3-cycles in the result.
- computeCliques(self, Comments=False)
- Computes all cliques, ie maximal complete subgraphs in self:
.. Note::
- Computes the maximal independent vertex sets in the dual of self.
- Result is stored in self.cliques.
- computeComponents(self)
- Computes the connected components of a graph instance.
Returns a partition of the vertices as a list
- computeDegreeDistribution(self, Comments=False)
- Renders the distribution of vertex degrees.
- computeDiameter(self, Oriented=False)
- Renders the diameter (maximal neighbourhood depth) of the digraph instance.
.. Note::
The diameter of a disconnected graph is considered to be *infinite*
(results in a value -1) !
- computeGirth(self, girthType='any', Comments=False)
- Renders the *girth* of self, i.e. the length of the shortest chordless cycle in the graph.
*Parameter*:
* *girthType* = "any" (default) | "odd" | "even"
- computeGraphCentres(self)
- Renders the vertices of minimal Neighborhood depth.
- computeMIS(self, Comments=False)
- Prints all maximal independent vertex sets:
.. Note::
- Result is stored in self.misset !
- computeMaximumMatching(self, Comments=False)
- Renders a maximum matching in *self* by computing
a maximum MIS of the line graph of *self*.
- computeNeighbourhoodDepth(self, vertex, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeNeighbourhoodDepthDistribution(self, Comments=False, Debug=False)
- Renders the distribtion of neighbourhood depths.
- computeOrientedDigraph(self, PartiallyDetermined=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the adjacent vertices' numbers.
If self is a PermutationGraph instance, the orientation will be transitive.
The parameter *PartiallyDetermined*: {True|False by default], converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,seed=101)
>>> dg = g.computeOrientedDigraph()
>>> dg
*------- Digraph instance description ------*
Instance class : Digraph
Instance name : oriented_randomGraph
Digraph Order : 6
Digraph Size : 5
Valuation domain : [-1.00; 1.00]
Determinateness : 100.000
Attributes : ['name','order','actions','valuationdomain',
'relation', 'gamma', 'notGamma',
'size', 'transitivityDegree']
>>> dg.transitivityDegree
Decimal('0.7142857142857142857142857143')
- computePermutation(self, seq1=None, seq2=None, Comments=True)
- Tests whether the graph instance *self* is a permutation graph
and renders, in case the test is positive,
the corresponding permutation.
- computeSize(self)
- Renders the number of positively characterised edges of this graph instance
(result is stored in self.size).
- computeTransitivelyOrientedDigraph(self, PartiallyDetermined=False, Debug=False)
- Renders a digraph where each edge of the permutation graph *self*
is converted into an arc oriented in increasing order of the ranks of implication classes
detected with the :py:func:`digraphs.Digraph.isComparabilityGraph` test and stored in self.edgeOrientations.
The parameter *PartiallyDetermined*: {True|False (by default), converts if *True* all absent
edges of the graph into indeterminate symmetric relations in the resulting digraph.
Verifies if the graph instance is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
>>> from graphs import RandomGraph
>>> g = RandomGraph(order=6,edgeProbability=0.5,seed=100)
>>> og = g.computeTransitivelyOrientedDigraph()
>>> if og is not None:
... print(og)
... print('Transitivity degree: %.3f' % og.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveDigraph
Instance name : trans_oriented_randomGraph
Digraph Order : 6
Digraph Size : 7
Valuation domain : [-1.00 - 1.00]
Determinateness : 46.667
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Transitivity degree: 1.000
>>> gd = -g
>>> ogd = gd.computeTransitivelyOrientedDigraph()
>>> if ogd is not None:
... print(ogd)
... print('Dual transitivity degree: %.3f' % ogd.transitivityDegree)
*------- Digraph instance description ------*
Instance class : TransitiveOrder
Instance name : trans_oriented_dual_randomGraph
Digraph Order : 6
Digraph Size : 8
Valuation domain : [-1.00 - 1.00]
Determinateness : 53.333
Attributes : ['name', 'order', 'actions',
'valuationdomain', 'relation',
'gamma', 'notGamma', 'size',
'transitivityDegree']
Dual transitivity degree: 1.000
- depthFirstSearch(self, Debug=False)
- Depth first search through a graph in lexicographical order
of the vertex keys.
- exportEdgeOrientationsGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', layout=None, arcColor='black', lineWidth=1, palette=1, bgcolor='cornsilk', Debug=False)
- Exports GraphViz dot file for oriented graph drawing filtering.
Example:
>>> from graphs import *
>>> g = RandomGraph(order=6,seed=100)
>>> if g.isComparabilityGraph():
... g.exportEdgeOrientationsGraphViz('orientedGraph')
.. image:: orientedGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportGraphViz(self, fileName=None, verticesSubset=None, Comments=True, graphType='png', graphSize='7,7', WithSpanningTree=False, WithVertexColoring=False, matching=None, layout=None, arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for graph drawing filtering.
Example:
>>> g = Graph(numberOfVertices=5,edgeProbability=0.3)
>>> g.exportGraphViz('randomGraph')
.. image:: randomGraph.png
:alt: Random graph
:width: 300 px
:align: center
- exportPermutationGraphViz(self, fileName=None, permutation=None, Comments=True, WithEdgeColoring=True, hspace=100, vspace=70, graphType='png', graphSize='7,7', arcColor='black', bgcolor='cornsilk', lineWidth=1)
- Exports GraphViz dot file for permutation drawing filtering.
Horizontal (default=100) and vertical (default=75) spaces betwen the vertices'
positions may be explicitely given in *hspace* and *vspace* parameters.
.. note::
If no *permutation* is provided, it is supposed to exist a self.permutation attribute.
- gammaSets(self, Debug=False)
- renders the gamma function as dictionary
- generateIndependent(self, U)
- Generator for all independent vertices sets
with neighborhoods of a graph instance:
.. note::
* Initiate with U = self._singletons().
* Yields [independent set, covered set, all vertices - covered set)].
* If independent set == (all vertices - covered set), the given independent set is maximal !
- graph2Digraph(self)
- Converts a Graph object into a symmetric Digraph object.
- isComparabilityGraph(self, Debug=False)
- Verifies if the graph instance is a comparability graph.
If yes, a tranditive orientation of the edges is stored
in self.edgeOrientations.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 129-132.
- isConnected(self)
- Cheks if self is a connected graph instance.
- isIntervalGraph(self, Comments=False)
- Checks whether the graph self is triangulated and
its dual is a comparability graph.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isPerfectGraph(self, Comments=False, Debug=False)
- A graph *g* is perfect when neither *g*, nor *-g*, contain any chordless
cycle of odd length.
- isPermutationGraph(self, Comments=False)
- Checks whether the graph self and
its dual are comparability graphs.
*Source*: M. Ch. Golumbic (2004) Algorithmic Graph Thery and Perfect Graphs,
Annals of Discrete Mathematics 57, Elsevier, p. 16.
- isSplitGraph(self, Comments=False)
- Checks whether the graph ' *self* ' and its dual ' *-self* ' are
triangulated graphs
- isTree(self)
- Checks if self is a tree by verifing the required number of
edges: order-1; and the existence of leaves.
- isTriangulated(self)
- Checks if a graph contains no chordless cycle of
length greater or equal to 4.
- randomDepthFirstSearch(self, seed=None, Debug=False)
- Depth first search through a graph in random order of the vertex keys.
.. Note::
The resulting spanning tree (or forest) is by far not uniformly selected
among all possible trees. Spanning stars will indeed be much less
probably selected then streight walks !
- recodeValuation(self, newMin=-1, newMax=1, ndigits=2, Debug=False)
- Recodes the characteristic valuation domain according
to the parameters given.
.. note::
Default values gives a normalized valuation domain
- save(self, fileName='tempGraph', Debug=False)
- Persistent storage of a Graph class instance in the form of a python source code file.
- setEdgeValue(self, edge, value, Comments=False)
- Wrapper for updating the characteristic valuation of a Graph instance.
The egde parameter consists in a pair of vertices;
edge = ('v1','v2') for instance.
The new value must be in the limits of the valuation domain.
- showCliques(self)
- showEdgesCharacteristicValues(self, ndigits=2)
- Prints the edge links of the bipartite graph instance
- showMIS(self)
- showMore(self)
- Generic show method for Graph instances.
- showShort(self)
- Generic show method for Graph instances.
Data descriptors inherited from graphs.Graph:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
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