Graphs
Authors
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Contributers of note: Alex Diaz, Luis Garcia, Shaowei Lin, Sonja Mapes, Mike Stillman, Doug Torrance
Version
This documentation describes version 0.3.2 of Graphs.
Source code
The source code from which this documentation is derived is in the file
Graphs.m2.
Exports
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Methods
- addEdge(Digraph,Set), see addEdge -- A method for adding edges to a graph
- addEdges'(Digraph,List), see addEdge -- A method for adding edges to a graph
- addEdges'(Graph,List) (missing documentation)
- addVertex(Digraph,Thing), see addVertex -- A method for adding a set of vertices to a graph
- addVertices(Digraph,List), see addVertex -- A method for adding a set of vertices to a graph
- addVertices(Graph,List) (missing documentation)
- adjacencyMatrix(Digraph), see adjacencyMatrix -- Returns the adjacency matrix of a Graph or Digraph
- barycenter(Graph), see barycenter -- Returns the barycenter of a grah
- bigraph(MixedGraph) (missing documentation)
- bipartiteColoring(Graph), see bipartiteColoring -- Returns a coloring of a bipartite graph
- breadthFirstSearch(Digraph,Thing), see breadthFirstSearch -- runs a breadth first search on the digraph starting at a specified node and returns a list of the vertices in the order they were discovered
- cartesianProduct(Graph,Graph), see cartesianProduct -- Computes the cartesian product of two graphs
- center(Graph), see center -- Returns the center of a graph
- children(Digraph,Thing), see children -- returns the children of a vertex of a digraph
- children(MixedGraph,Thing) (missing documentation)
- chromaticNumber(Graph), see chromaticNumber -- Computes the chromatic number of a graph
- cliqueComplex(Graph), see cliqueComplex -- Returns the clique complex of a graph
- cliqueNumber(Graph), see cliqueNumber -- Returns the clique number of a graph
- closedNeighborhood(Graph,Thing), see closedNeighborhood -- Returns the closed neighborhood of a vertex of a graph
- clusteringCoefficient(Graph) (missing documentation)
- clusteringCoefficient(Graph,Thing) (missing documentation)
- collateVertices(MixedGraph) (missing documentation)
- complementGraph(Graph), see complementGraph -- Returns the complement of a graph
- connectedComponents(Graph), see connectedComponents -- Computes the connected components of a graph
- coverIdeal(Graph), see coverIdeal -- Returns the vertex cover ideal of a graph
- criticalEdges(Graph), see criticalEdges -- Finds the critical edges of a graph
- degeneracy(Graph), see degeneracy -- Computes the degeneracy of a graph
- degree(Digraph,Thing) -- returns the degree of a vertex in a digraph
- degree(Graph,Thing) (missing documentation)
- degreeCentrality(Graph,Thing), see degreeCentrality -- Returns the degreeCentrality of a vertex of a graph
- degreeIn(Digraph,Thing), see degreeIn -- returns the "in-degree" of a vertex in a digraph
- degreeMatrix(Digraph), see degreeMatrix -- Returns the degree matrix of a graph
- degreeOut(Digraph,Thing), see degreeOut -- returns the "out-degree" of a vertex in a digraph
- deleteEdges(Graph,List), see deleteEdges -- Deletes a list of edges from a graph
- deleteEdges(Digraph,List) (missing documentation)
- deleteVertex(Graph,Thing), see deleteVertex -- a method for deleting the vertex of a graph
- deleteVertex(Digraph,Thing) (missing documentation)
- deleteVertices(Digraph,List), see deleteVertices -- Deletes specified vertices from a digraph or graph
- density(Graph), see density -- computes the density of a graph
- depthFirstSearch(Digraph), see depthFirstSearch -- runs a depth first search on the digraph or digraph and returns the discovery time and finishing time for each vertex in the digraph
- descendants(Digraph,Thing), see descendants -- returns the descendants of a digraph
- descendants(MixedGraph,Thing) (missing documentation)
- diameter(Graph), see diameter -- Computes the diameter of a graph
- Digraph _ List (missing documentation)
- Digraph _ ZZ (missing documentation)
- Digraph _* (missing documentation)
- digraph(MixedGraph) (missing documentation)
- digraphTranspose(Digraph), see digraphTranspose -- returns the transpose of a Digraph
- directProduct(Graph,Graph), see directProduct -- Computes the direct product of two graphs
- displayGraph(Digraph), see displayGraph -- displays a digraph or graph using Graphviz
- displayGraph(String,Digraph), see displayGraph -- displays a digraph or graph using Graphviz
- displayGraph(String,String,Digraph), see displayGraph -- displays a digraph or graph using Graphviz
- distance(Digraph,Thing,Thing), see distance -- Computes the distance between two vertexSet in a graph
- distance(Digraph,Thing) (missing documentation)
- distanceMatrix(Digraph), see distanceMatrix -- Computes the distance matrix of a digraph
- eccentricity(Graph,Thing), see eccentricity -- Returns the eccentricity of a vertex of a graph
- edgeConnectivity(Graph), see edgeConnectivity -- computes the edge connectivity of a graph
- edgeCuts(Graph), see edgeCuts -- returns the edge cuts of a graph
- edgeIdeal(Graph), see edgeIdeal -- returns the edge ideal of a graph
- edges(Digraph), see edges -- Returns the edges of a digraph or graph
- edges(Graph), see edges -- Returns the edges of a digraph or graph
- expansion(Graph), see expansion -- returns the expansion of a graph
- findPaths(Digraph,Thing,ZZ), see findPaths -- finds all the paths in a digraph of a given length starting at a given vertex
- floydWarshall(Digraph), see floydWarshall -- runs the Floyd-Warshall algorithm on a digraph to determine the minimum distance from one vertex to another in the digraph
- forefathers(Digraph,Thing), see forefathers -- returns the forefathers of a digrah
- forefathers(MixedGraph,Thing) (missing documentation)
- girth(Graph), see girth -- A method for computing the girth of a graph
- graph(Digraph) -- Returns the legacy G#graph hash table
- graph(LabeledGraph) (missing documentation)
- graph(MixedGraph) (missing documentation)
- graphComposition(Graph,Graph), see graphComposition -- A method for composing two graphs
- graphPower(Graph,ZZ), see graphPower -- constructs a graph raised to a power
- hasEulerianTrail(Digraph), see hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail
- hasEulerianTrail(Graph), see hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail
- hasOddHole(Graph), see hasOddHole -- checks whether a graph has a odd hole
- incidenceMatrix(Graph), see incidenceMatrix -- computes the incidence matrix of a graph
- independenceComplex(Graph), see independenceComplex -- constructs the independence complex of a graph
- independenceNumber(Graph), see independenceNumber -- computes the independence number of a graph
- indexLabelGraph(Digraph), see indexLabelGraph -- Relabels the vertices of a graph or digraph according to their indices, indexed from 0.
- indexLabelGraph(Graph), see indexLabelGraph -- Relabels the vertices of a graph or digraph according to their indices, indexed from 0.
- inducedSubgraph(Digraph,List), see inducedSubgraph -- A method for finding the induced subgraph of any Graph or Digraph
- inducedSubgraph(Graph,List), see inducedSubgraph -- A method for finding the induced subgraph of any Graph or Digraph
- isBipartite(Graph), see isBipartite -- determines whether a graph is bipartite
- isChordal(Graph), see isChordal -- checks whether a graph is chordal
- isCM(Graph), see isCM -- determines if a graph is Cohen-Macaulay
- isConnected(Graph), see isConnected -- determines whether a graph is connected
- isCyclic(Graph), see isCyclic -- determines whether a graph is cyclic
- isCyclic(Digraph) -- determines whether a digraph is cyclic
- isEulerian(Digraph), see isEulerian -- determines if a graph or digraph is Eulerian
- isEulerian(Graph), see isEulerian -- determines if a graph or digraph is Eulerian
- isForest(Graph), see isForest -- determines whether a graph is a forest
- isLeaf(Graph,Thing), see isLeaf -- determines whether a vertex is a leaf
- isPerfect(Graph), see isPerfect -- checks whether a graph is perfect
- isReachable(Digraph,Thing,Thing), see isReachable -- checks if a vertex u is reachable from a vertex v
- isRegular(Graph), see isRegular -- determines whether a graph is regular
- isRigid(Graph), see isRigid -- checks if a graph is rigid
- isSimple(Graph), see isSimple -- checks if a graph is simple
- isSink(Digraph,Thing), see isSink -- determines if a vertex of a digraph is a sink or not
- isSource(Digraph,Thing), see isSource -- determines if a vertex of a digraph is a source or not
- isStronglyConnected(Digraph), see isStronglyConnected -- checks if a digraph is strongly connected
- isTree(Graph), see isTree -- determines whether a graph is a tree
- isWeaklyConnected(Digraph), see isWeaklyConnected -- checks if a digraph is weakly connected
- labeledGraph(Digraph,List) (missing documentation)
- laplacianMatrix(Graph), see laplacianMatrix -- Returns the laplacian matrix of a graph
- leaves(Graph), see leaves -- lists the leaves of a tree graph
- lineGraph(Graph), see lineGraph -- Returns the line graph of an undirected graph
- lowestCommonAncestors(Digraph,Thing,Thing), see lowestCommonAncestors -- determines the lowest common ancestors between two vertexSet
- minimalDegree(Graph), see minimalDegree -- computes the minimal degree of a graph
- minimalVertexCuts(Graph), see minimalVertexCuts -- finds the minimal vertex cuts of a graph
- mixedGraph(Digraph) (missing documentation)
- mixedGraph(Digraph,Bigraph) (missing documentation)
- mixedGraph(Graph,Digraph) (missing documentation)
- mixedGraph(Graph,Digraph,Bigraph) (missing documentation)
- neighbors(Graph,Thing), see neighbors -- returns the neighbors of a vertex in a graph
- neighbors(MixedGraph,Thing) (missing documentation)
- net(Digraph) (missing documentation)
- net(LabeledGraph) (missing documentation)
- net(MixedGraph) (missing documentation)
- nondescendants(Digraph,Thing), see nondescendants -- returns the nondescendants of a vertex of a digraph
- nondescendants(MixedGraph,Thing) (missing documentation)
- nonneighbors(Graph,Thing), see nonneighbors -- returns the non-neighbors of a vertex in a graph
- nonneighbors(MixedGraph,Thing) (missing documentation)
- numberOfComponents(Graph), see numberOfComponents -- computes the number of connected components of a graph
- numberOfTriangles(Graph), see numberOfTriangles -- counts how many subtriangles are present in a graph
- parents(Digraph,Thing), see parents -- returns the parents of a vertex on a digraph
- parents(MixedGraph,Thing) (missing documentation)
- radius(Graph), see radius -- Returns the radius of a graph
- reachable(Digraph,List), see reachable -- Returns the vertices reachable in a digraph from a given collection of vertices
- reachable(Digraph,Set), see reachable -- Returns the vertices reachable in a digraph from a given collection of vertices
- reindexBy(Digraph,String), see reindexBy -- reindexes the vertices according to the input ordering.
- reindexBy(Graph,String), see reindexBy -- reindexes the vertices according to the input ordering.
- reverseBreadthFirstSearch(Digraph,Thing), see reverseBreadthFirstSearch -- runs a reverse breadth first search on the digraph and returns a list of the vertexSet in the order they were discovered
- showTikZ(Digraph), see showTikZ -- Writes a string of TikZ syntax that can be pasted into a .tex file to display G
- sinks(Digraph), see sinks -- returns the sinks of a digraph
- sources(Digraph), see sources -- returns the sources of a digraph
- spanningForest(Graph), see spanningForest -- constructs a spanning forest of a graph
- spectrum(Graph), see spectrum -- Returns the spectrum of a graph
- strongProduct(Graph,Graph), see strongProduct -- a method for taking the strong product of two graphs
- topologicalSort(Digraph) (missing documentation)
- topologicalSort(Digraph,String) (missing documentation)
- topSort(Digraph) (missing documentation)
- toString(Digraph) (missing documentation)
- toString(LabeledGraph) (missing documentation)
- toString(MixedGraph) (missing documentation)
- underlyingGraph(Digraph), see underlyingGraph -- Returns the underlying graph of a digraph
- vertexConnectivity(Graph), see vertexConnectivity -- computes the vertex connectivity of a graph
- vertexCoverNumber(Graph), see vertexCoverNumber -- returns the vertex cover number of a graph
- vertexCovers(Graph), see vertexCovers -- returns a list of the minimal vertex covers of a graph
- vertexCuts(Graph), see vertexCuts -- lists all the vertex cuts of a graph
- vertexMultiplication(Graph,Thing,Thing), see vertexMultiplication
- vertexSet(Digraph), see vertexSet -- Returns the vertices of a graph or digraph
- vertices(Digraph), see vertexSet -- Returns the vertices of a graph or digraph
- vertices(MixedGraph) (missing documentation)
- writeDotFile(String,Graph), see writeDotFile -- Writes a graph to a dot file with a specified filename
Symbols
- discoveryTime (missing documentation)
- EntryMode (missing documentation)
- finishingTime (missing documentation)
- newDigraph (missing documentation)
- simpleGraph (missing documentation)
- Singletons (missing documentation)