Compositions[n, k] gives a list of all compositions of integer n into k parts.

FindCycle[g] finds a list of vertices that define a cycle in graph g.

GraphicQ[s] yields True if the list of integers s is a graphic sequence, and thus represents a degree sequence of some graph.

Neighborhood[g, v, k] returns the subset of vertices in g that are at a distance of k or less from vertex v. Neighborhood[al, v, k] behaves identically, except that it takes ...

NormalizeVertices[v] gives a list of vertices with a similar embedding as v but with the coordinates of all points scaled to be between 0 and 1.

RotateVertices[v, \[Theta]] rotates each vertex position in list v by \[Theta] radians about the origin (0, 0). RotateVertices[g, \[Theta]] rotates the embedding of the graph ...

SamenessRelation[l] constructs a binary relation from a list l of permutations, which is an equivalence relation if l is a permutation group.

ToCycles[p] gives the cycle structure of permutation p as a list of cyclic permutations.

TranslateVertices[v, {x, y}] adds the vector {x, y} to the vertex embedding location of each vertex in list v. TranslateVertices[g, {x, y}] translates the embedding of the ...

TwoColoring[g] finds a two-coloring of graph g if g is bipartite. It returns a list of the labels 1 and 2 corresponding to the vertices.