GetVertexLabels[g] returns the list of labels of vertices of g. GetVertexLabels[g, v] returns the list of labels in graph g of the vertices specified in list v.

GetVertexWeights[g] returns the list of weights of vertices of g. GetVertexWeights[g, v] returns the list of weights in graph g of the vertices in v.

Girth[g] gives the length of a shortest cycle in a simple graph g.

MinimumSpanningTree[g] uses Kruskal's algorithm to find a minimum spanning tree of graph g.

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.

TopologicalSort[g] gives a permutation of the vertices of the directed acyclic graph g such that an edge (i, j) implies that vertex i appears before vertex j.

LayerSizeFunction is an option for TreePlot that gives a function to specify the relative height to allow for each layer.

NumberOfDirectedGraphs[n] returns the number of nonisomorphic directed graphs with n vertices. NumberOfDirectedGraphs[n, m] returns the number of nonisomorphic directed ...

NumberOfGraphs[n] returns the number of nonisomorphic undirected graphs with n vertices. NumberOfGraphs[n, m] returns the number of nonisomorphic undirected graphs with n ...

IndependentVertexSetQ[g, vlist] yields True if the vertex list vlist is an independent vertex set in the graph g and False otherwise.