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

Backtrack[s, partialQ, solutionQ] performs a backtrack search of the state space s, expanding a partial solution so long as partialQ is True and returning the first complete ...

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 ...

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

Bridges[g] gives a list of the bridges of graph g, where each bridge is an edge whose removal disconnects the graph.

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.

CompleteQ[g] yields True if graph g is complete. This means that between any pair of vertices there is an undirected edge or two directed edges going in opposite directions.