CompleteKaryTree[n, k] returns a complete k-ary tree on n vertices.

Contract[g, {x, y}] gives the graph resulting from contracting the pair of vertices {x, y} of graph g.

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

DegreeSequence[g] gives the sorted degree sequence of graph g.

DeleteVertex[g, v] deletes a single vertex v from graph g. Here v is a vertex number.

DeleteVertices[g, vList] deletes vertices in vList from graph g. vList has the form {i, j, ...}, where i, j, ... are vertex numbers.

EquivalenceClasses[r] identifies the equivalence classes among the elements of matrix r.

EquivalenceRelationQ[r] yields True if the matrix r defines an equivalence relation. EquivalenceRelationQ[g] tests whether the adjacency matrix of graph g defines an ...

FiniteGraphs produces a convenient list of all the interesting, finite, parameterless graphs built into Combinatorica.

GetEdgeLabels[g] returns the list of labels of the edges of g. GetEdgeLabels[g, e] returns the list of labels in graph g of the edges in e.