# Digraph

## Functions and methods returning a digraph :

• "addVertex(Digraph,Thing)" -- see addVertex -- A method for adding a set of vertices to a graph
• deleteVertex(Digraph,Thing) (missing documentation)
• "deleteVertices(Digraph,List)" -- see deleteVertices -- Deletes specified vertices from a digraph or graph
• "digraph(HashTable)" -- see digraph -- Constructs a digraph
• "digraph(List)" -- see digraph -- Constructs a digraph
• "digraph(List,List)" -- see digraph -- Constructs a digraph
• "digraph(List,Matrix)" -- see digraph -- Constructs a digraph
• "digraph(Matrix)" -- see digraph -- Constructs a digraph
• "digraphTranspose(Digraph)" -- see digraphTranspose -- returns the transpose of a Digraph
• "indexLabelGraph(Digraph)" -- 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
• "reindexBy(Digraph,String)" -- see reindexBy -- reindexes the vertices according to the input ordering.

## Methods that use a digraph :

• "addVertices(Digraph,List)" -- see addVertex -- A method for adding a set of vertices to a 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
• "children(Digraph,Thing)" -- see children -- returns the children of a vertex of a digraph
• degree(Digraph,Thing) -- returns the degree of a vertex in a digraph
• "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(Digraph,List) (missing documentation)
• "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
• Digraph _ List (missing documentation)
• Digraph _ ZZ (missing documentation)
• Digraph _* (missing documentation)
• "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
• "edges(Digraph)" -- see edges -- Returns the edges of a digraph or 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 digraph
• graph(Digraph) -- Returns the legacy G#graph hash table
• "hasEulerianTrail(Digraph)" -- see hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail
• html(Digraph) -- Create an .svg representation of a graph or digraph
• isCyclic(Digraph) -- determines whether a digraph is cyclic
• "isEulerian(Digraph)" -- see isEulerian -- determines if a graph or digraph is Eulerian
• "isReachable(Digraph,Thing,Thing)" -- see isReachable -- checks if a vertex u is reachable from a vertex v
• "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
• "isWeaklyConnected(Digraph)" -- see isWeaklyConnected -- checks if a digraph is weakly connected
• "lowestCommonAncestors(Digraph,Thing,Thing)" -- see lowestCommonAncestors -- determines the lowest common ancestors between two vertexSet
• net(Digraph) (missing documentation)
• "nondescendants(Digraph,Thing)" -- see nondescendants -- returns the nondescendants of a vertex of a digraph
• "parents(Digraph,Thing)" -- see parents -- returns the parents of a vertex on a digraph
• "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
• "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
• "topologicalSort(Digraph)" -- see topologicalSort -- outputs a list of vertices in a topologically sorted order of a DAG.
• "topologicalSort(Digraph,String)" -- see topologicalSort -- outputs a list of vertices in a topologically sorted order of a DAG.
• "topSort(Digraph)" -- see topSort -- outputs a hashtable containing original digraph, new digraph with vertices topologically sorted and a map from vertices of original digraph to new digraph.
• "topSort(Digraph,String)" -- see topSort -- outputs a hashtable containing original digraph, new digraph with vertices topologically sorted and a map from vertices of original digraph to new digraph.
• toString(Digraph) (missing documentation)
• "underlyingGraph(Digraph)" -- see underlyingGraph -- Returns the underlying graph of a digraph
• "vertexSet(Digraph)" -- see vertexSet -- Returns the vertices of a graph or digraph
• "vertices(Digraph)" -- see vertexSet -- Returns the vertices of a graph or digraph
• "writeDotFile(String,Digraph)" -- see writeDotFile -- Writes a graph to a dot file with a specified filename

## For the programmer

The object Digraph is a type, with ancestor classes HashTable < Thing.