InversePermutation[p] yields the multiplicative inverse of permutation p.

Inversions[p] counts the number of inversions in permutation p.

LineGraph[g] constructs the line graph of graph g.

LongestIncreasingSubsequence[p] finds the longest increasing scattered subsequence of permutation p.

MakeSimple[g] gives the undirected graph, free of multiple edges and self-loops derived from graph g.

MaximumAntichain[g] gives a largest set of unrelated vertices in partial order g.

MaximumIndependentSet[g] finds a largest independent set of graph g.

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

MinimumChainPartition[g] partitions partial-order g into a minimum number of chains.

MultipleEdgesQ[g] yields True if g has multiple edges between pairs of vertices. It yields False otherwise.