MakeUndirected[g] gives the underlying undirected graph of the given directed graph g.

MinimumSpanningTree[g] uses Kruskal's algorithm to find a minimum spanning tree of graph g.

MinimumVertexCover[g] finds a minimum vertex cover of graph g.

M[g] gives the number of edges in the graph g. M[g, Directed] is obsolete because M[g] works for directed as well as undirected graphs.

NumberOfTableaux[p] uses the hook length formula to count the number of Young tableaux with shape defined by partition p.

OrientGraph[g] assigns a direction to each edge of a bridgeless, undirected graph g, so that the graph is strongly connected.

ParentsToPaths[l, i, j] takes a list of parents l and returns the path from i to j encoded in the parent list. ParentsToPaths[l, i] returns the paths from i to all vertices.

PartialOrderQ[g] yields True if the binary relation defined by edges of the graph g is a partial order, meaning it is transitive, reflexive, and antisymmetric. ...

PartitionQ[p] yields True if p is an integer partition. PartitionQ[n, p] yields True if p is a partition of n.

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.