CostOfPath[g, p] sums up the weights of the edges in graph g defined by the path p.

DegreesOf2Neighborhood[g, v] returns the sorted list of degrees of vertices of graph g within a distance of 2 from v.

EmptyQ[g] yields True if graph g contains no edges.

ExtractCycles[g] gives a maximal list of edge-disjoint cycles in graph g.

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

NumberOfSpanningTrees[g] gives the number of labeled spanning trees of graph g.

PlanarQ[g] yields True if graph g is planar, meaning it can be drawn in the plane so no two edges cross.

PseudographQ[g] yields True if graph g is a pseudograph, meaning it contains self-loops.

Radius[g] gives the radius of graph g, the minimum eccentricity of any vertex of g.

SelfComplementaryQ[g] yields True if graph g is self-complementary, meaning it is isomorphic to its complement.