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.

LoopPosition is an option to ShowGraph whose values tell ShowGraph where to position a loop around a vertex. This option can take on values UpperLeft, UpperRight, LowerLeft, ...

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.

OrientGraph[g] assigns a direction to each edge of a bridgeless, undirected graph g, so that the graph is strongly connected.

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. ...

PerfectQ[g] yields True if g is a perfect graph, meaning that for every induced subgraph of g the size of a largest clique equals the chromatic number.

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.

RadialEmbedding[g, v] constructs a radial embedding of the graph g in which vertices are placed on concentric circles around v depending on their distance from v. ...

RandomKSetPartition[set, k] returns a random set partition of set with k blocks. RandomKSetPartition[n, k] returns a random set partition of the first n natural numbers into ...

RandomRGF[n] returns a random restricted growth function (RGF) defined on the first n natural numbers. RandomRGF[n, k] returns a random RGF defined on the first n natural ...