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A hypergraph is a collection of hyperedges. A hyperedge is a set of vertices.
The base set is defined implicitly as the union of the hyperedges.
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| Boolean |
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| Boolean |
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| Boolean |
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| Set |
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| Iterator |
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| Boolean |
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| Int |
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| Boolean |
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| String |
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| String |
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The same as self
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| GraphCanvas |
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| List |
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| Boolean |
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| Boolean |
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| Boolean |
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| Boolean |
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| Boolean |
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| Boolean |
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| Boolean or set |
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| Boolean |
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| Boolean |
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| ReducedHypergraph |
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| Graphs.UForest |
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| Graphs.UForest |
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| Tuple |
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| Tuple |
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False or Tuple, a pair of dictionaries
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| Int |
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| Set |
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| Int |
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| List |
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| Dictionary |
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Same class as self
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| UGraph |
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| List |
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| list of frozensets |
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| Int |
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| Set |
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| Int |
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| Set |
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| UGraph |
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| Set |
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Inherited from Inherited from |
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| Dictionary |
_extras If repeated hyperedges exist, maps each repeated hyperedge to the number of times it is repeated. |
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_hyperedges The distinct hyperedges in the hypergraph. |
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| Dictionary |
_star Maps a vertex to the set of hyperedges which contain it. |
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Inherited from |
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Initialise a hypergraph
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Return whether a hyperedge is in the hypergraph
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Return whether Irrespective of class
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Return whether
Irrespective of class
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Return the star of Altering the returned set will alter the hypergraph, so don't do it! A safer option is to use the star method. Note that a set object is returned, not a hypergraph object.
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Return an iterator over the distinct hyperedges in the hypergraph To allow
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Return whether
Irrespective of class
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Return the number of hyperedges in the hypergraph
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Return whether Irrespective of class
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Return 'official' string representation of the hypergraph Can be used to construct the hypergraph using e.g.
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Return pretty representation of a hypergraph
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Add a hyperedge
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Return a deep copy of the hypergraph
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Remove a hyperedge (and any repetitions), or do nothing if the hyperedge does not exist
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For each hyperedge in
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Remove
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Remove
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Return the dual of the hypergraph To Do: make more efficient |
Run Graham's algorithm on a hypergraph If the hypergraph is decomposable then upon return |
Display a hypergraph using a GUI Shows the representative graph Ignores repeated hyperedges, so not quite accurate for non-simple hypergraphs
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Return a list of the hyperedges in the hypergraph
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Return whether the hypergraph is arboreal A hypergraph is arboreal iff its dual is acyclic (ie decomposable)
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Return whether the hypergraph is decomposable Uses maximum_cardinality_search
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Return whether the hypergraph is decomposable Uses maximum_cardinality_search
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Return whether the hypergraph is graphical
To Do: Implement efficiently |
Return whether the hypergraph is graphical
To Do: Implement efficiently |
Test whether a hypergraph is reduced
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Whether
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Whether the hypergraph is a separating hypergraph A hypergraph is separating if, for every vertex v, the intersection of all hyperedges in v's star equals {v}
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Test whether a hypergraph is simple
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Return the join of
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Return a join forest graph, assuming decomposability Any repeated hyperedges are ignored Uses maximum_cardinality_search. See that method for bibliographical references.
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Return a join forest for the hypergraph using vertex elimination Source is annotated. Refs:
@TechReport{graham79,
author = {M. H. Graham},
title = {On the universal relation},
institution = {University of Toronto},
year = 1979,
address = {Toronto, Canada}
}
@article{322389,
author = {Catriel Beeri and Ronald Fagin and David Maier and Mihalis Yannakakis},
title = {On the Desirability of Acyclic Database Schemes},
journal = {Journal of the {ACM}},
volume = {30},
number = {3},
year = {1983},
issn = {0004-5411},
pages = {479--513},
doi = {http://doi.acm.org/10.1145/2402.322389},
publisher = {ACM Press},
address = {New York, NY, USA},
}
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Return a DecomposableHypergraph produced by eliminating variables
from Destroys
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Return a DecomposableHypergraph produced by eliminating variables
from Destroys If no
To Do: This is simple but inefficient at present. |
True if ... irrespective of whether
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Multiple hyperedges are ignored, so if the hypergraph is non-simple this produces the same result as if multiple hyperedges had been deleted.
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Replace hyperedges by their union. All repetitions of a hyperedge in
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Return how often Returns 0 if
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Return the set of all those vertices each of which is in a hyperedge
with
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Return the number of vertices in the hypergraph
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Reduce the hypergraph Does not change the class of Any hyperedge contained in another is removed
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Returns a dictionary mapping, by default, each distinct redundant hyperedge to the set of distinct hyperedges which properly contain it. A strictly redundant hyperedge is one properly contained in another
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Remove a hyperedge (including any repetitions of it)
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Remove one occurrence of a hyperedge If the hyperedge is repeated a repetition is removed.
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Remove distinct hyperedges Each hyperedge in
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Remove
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Remove
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Rename the vertices of a hypergraph New hypergraph is isomorphic to existing one.
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Return the representative graph of a hypergraph The vertices of the graph are hyperedges of the hypergraph. Two vertices are connected if the corresponding hyperedges intersect Ignores repeated hyperedges, so not quite accurate for non-simple hypergraphs Also known as the line-graph of the hypergraph
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Restrict the hypergraph to contain only
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Simplify a hypergraph Returning repeated hyperedges deleted
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Return the number of hyperedges in the hypergraph
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Return the star of Altering the returned set will not alter the hypergraph. Note that a set object is returned, not a hypergraph object.
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Return a count of the number of distinct hyperedges containing a vertex
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Return the hyperedges each of which contain at least one vertex in
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Return the 2-section of a hypergraph This graph contains an undirected edge for any pair of distinct vertices which are both members of a hyperedge.
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Return the vertices (base set) of the hypergraph
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Whether If
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_extrasIf repeated hyperedges exist, maps each repeated hyperedge to the number of times it is repeated. (If repeated once, the hyperedge occurs twice.)
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_hyperedgesThe distinct hyperedges in the hypergraph. Each hyperedge is a frozenset
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_starMaps a vertex to the set of hyperedges which contain it. (Effectively represents the dual hypergraph.)
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