RandomSetPartition[set] returns a random set partition of set. RandomSetPartition[n] returns a random set partition of the first n natural numbers.

SetPartitionQ[sp, s] determines if sp is a set partition of set s. SetPartitionQ[sp] tests if sp is a set of disjoint sets.

ShakeGraph[g, d] performs a random perturbation of the vertices of graph g, with each vertex moving, at most, a distance d from its original position.

ShowGraphArray[{g_1, g_2, ...}] displays a row of graphs. ShowGraphArray[{{g_1, ...}, {g_2, ...}, \ ...}] displays a two-dimensional table of graphs.

TransposePartition[p] reflects a partition p of k parts along the main diagonal, creating a partition with maximum part k.

TreeToCertificate[t] returns a binary string that is a certificate for the tree t such that trees have the same certificate if and only if they are isomorphic.

UnrankSetPartition[r, s, k] finds a k-block set partition of s with rank r. UnrankSetPartition[r, n, k] finds a k-block set partition of {1, 2, ..., n} with rank r.

UnrankSetPartition[r, set] finds a set partition of set with rank r. UnrankSetPartition[r, n] finds a set partition of {1, 2, ..., n} with rank r.

VertexLabelPosition is an option that allows the user to place a vertex label in a certain position relative to the vertex.

VertexNumberPosition is an option that can be used in ShowGraph to display a vertex number in a certain position relative to the vertex.