PlanarQ[g] yields True if graph g is planar, meaning it can be drawn in the plane so no two edges cross.

PseudographQ[g] yields True if graph g is a pseudograph, meaning it contains self-loops.

ReflexiveQ[g] yields True if the adjacency matrix of g represents a reflexive binary relation.

RegularGraph[k, n] constructs a semirandom k-regular graph on n vertices, if such a graph exists.

RegularQ[g] yields True if g is a regular graph.

RGFQ[l] yields True if l is a restricted growth function. It yields False otherwise.

SelfComplementaryQ[g] yields True if graph g is self-complementary, meaning it is isomorphic to its complement.

SelfLoopsQ[g] yields True if graph g has self-loops.

SimpleQ[g] yields True if g is a simple graph, meaning it has no multiple edges and contains no self-loops.

Strong is an option to ConnectedQ that seeks to determine if a directed graph is strongly connected.