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.

TransitiveReduction[g] finds a smallest graph that has the same transitive closure as g.

TravelingSalesman[g] finds an optimal traveling salesman tour in graph g.

TriangleInequalityQ[g] yields True if the weights assigned to the edges of graph g satisfy the triangle inequality.

V[g] gives the order or number of vertices of the graph g.

WriteGraph[g, f] writes graph g to file f using an edge list representation.

Cycle[n] constructs the cycle on n vertices, the 2-regular connected graph. An option Type that takes on values Directed or Undirected is allowed. The default setting is Type ...

ShowLabeledGraph[g] displays graph g according to its embedding, with each vertex labeled with its vertex number.ShowLabeledGraph[g, l] uses the i\[Null]^th element of list l ...

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.