HamiltonianQ[g] yields True if there exists a Hamiltonian cycle in graph g, or in other words, if there exists a cycle that visits each vertex exactly once.

PartialOrderQ[g] yields True if the binary relation defined by edges of the graph g is a partial order, meaning it is transitive, reflexive, and antisymmetric. ...

PartitionQ[p] yields True if p is an integer partition. PartitionQ[n, p] yields True if p is a partition of n.

SetEdgeLabels[g, l] assigns the labels in l to edges of g.

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

SetVertexLabels[g, l] assigns the labels in l to vertices of g.

SymmetricQ[r] tests if a given square matrix r represents a symmetric relation. SymmetricQ[g] tests if the edges of a given graph represent a symmetric relation.

TransitiveClosure[g] finds the transitive closure of graph g, the supergraph of g that contains edge {x, y} if and only if there is a path from x to y.

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.

The functionality of PrimitiveElement is now available in the newly added built-in Mathematica kernel function ToNumberField.