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 ...

FromAdjacencyLists[l] constructs an edge list representation for a graph from the given adjacency lists l, using a circular embedding. FromAdjacencyLists[l, v] uses v as the ...

FromOrderedPairs[l] constructs an edge list representation from a list of ordered pairs l, using a circular embedding. FromOrderedPairs[l, v] uses v as the embedding for the ...

FromUnorderedPairs[l] constructs an edge list representation from a list of unordered pairs l, using a circular embedding.FromUnorderedPairs[l, v] uses v as the embedding for ...

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, ...

GridGraph[n, m] constructs an n*m grid graph, the product of paths on n and m vertices. GridGraph[p, q, r] constructs a p*q*r grid graph, the product of GridGraph[p, q] and a ...

KSubsetGroup[pg, s] returns the group induced by a permutation group pg on the set s of k-subsets of [n], where n is the index of pg. The optional argument Type can be ...

MakeDirected[g] constructs a directed graph from a given undirected graph g by replacing each undirected edge in g by two directed edges pointing in opposite directions.

Orbits[pg, x] returns the orbits of x induced by the action of the group pg on x.

RandomGraph[n, p] constructs a random labeled graph on n vertices with an edge probability of p.