NetworkFlow[g, source, sink] returns the value of a maximum flow through graph g from source to sink. NetworkFlow[g, source, sink, Edge] returns the edges in g that have ...

GraphPolynomial[n, x] returns a polynomial in x in which the coefficient of x^m is the number of nonisomorphic graphs with n vertices and m edges. GraphPolynomial[n, x, ...

BellmanFord[g, v] gives a shortest-path spanning tree and associated distances from vertex v of graph g. The shortest-path spanning tree is given by a list in which element i ...

BooleanAlgebra[n] gives a Hasse diagram for the Boolean algebra on n elements. The function takes two options: Type and VertexLabel, with default values Undirected and False, ...

ConnectedQ[g] yields True if undirected graph g is connected. If g is directed, the function returns True if the underlying undirected graph is connected. ConnectedQ[g, ...

Dijkstra[g, v] gives a shortest-path spanning tree and associated distances from vertex v of graph g. The shortest-path spanning tree is given by a list in which element i is ...

DominationLattice[n] returns a Hasse diagram of the partially ordered set on integer partitions of n in which p < q if q dominates p. The function takes two options: Type and ...

ToAdjacencyMatrix[g] constructs an adjacency matrix representation for graph g. ToAdjacencyMatrix[g, EdgeWeight] returns edge weights as entries of the adjacency matrix with ...

ToOrderedPairs[g] constructs a list of ordered pairs representing the edges of the graph g.

ToUnorderedPairs[g] constructs a list of unordered pairs representing the edges of graph g. Each edge, directed or undirected, results in a pair in which the smaller vertex ...