Distances[g, v] returns the distances in nondecreasing order from vertex v to all vertices in g, treating g as an unweighted graph.

DominatingIntegerPartitionQ[a, b] yields True if integer partition a dominates integer partition b, that is, the sum of a size-t prefix of a is no smaller than the sum of a ...

Eccentricity[g] gives the eccentricity of each vertex v of graph g, the maximum length among all shortest paths from v.

FindSet[n, s] gives the root of the set containing n in union-find data structure s.

Girth[g] gives the length of a shortest cycle in a simple graph g.

GraphCenter[g] gives a list of the vertices of graph g with minimum eccentricity.

HasseDiagram[g] constructs a Hasse diagram of the relation defined by directed acyclic graph g.

IdenticalQ[g, h] yields True if graphs g and h have identical edge lists, even though the associated graphics information need not be the same.

InitializeUnionFind[n] initializes a union-find data structure for n elements.

IsomorphismQ[g, h, p] tests if permutation p defines an isomorphism between graphs g and h.