AntiSymmetricQ[g] yields True if the adjacency matrix of g represents an anti-symmetric binary relation.

ArticulationVertices[g] gives a list of all articulation vertices in graph g. These are vertices whose removal will disconnect the graph.

BiconnectedComponents[g] gives a list of the biconnected components of graph g. If g is directed, the underlying undirected graph is used.

BiconnectedQ[g] yields True if graph g is biconnected. If g is directed, the underlying undirected graph is used.

BipartiteMatchingAndCover[g] takes a bipartite graph g and returns a matching with maximum weight along with the dual vertex cover. If the graph is not weighted, it is ...

BipartiteMatching[g] gives the list of edges associated with a maximum matching in bipartite graph g. If the graph is edge weighted, then the function returns a matching with ...

BrelazColoring[g] returns a vertex coloring in which vertices are greedily colored with the smallest available color in decreasing order of vertex degree.

ChromaticPolynomial[g, z] gives the chromatic polynomial P(z) of graph g, which counts the number of ways to color g with, at most, z colors.

CoarserSetPartitionQ[a, b] yields True if set partition b is coarser than set partition a; that is, every block in a is contained in some block in b.

CodeToLabeledTree[l] constructs the unique labeled tree on n vertices from the Prüfer code l, which consists of a list of n - 2 integers between 1 and n.