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.

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 ...

There are many convenient ways to get an image into Mathematica , including drag and drop. You can also import images by evaluating commands in a notebook. Once you have an ...

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

VertexIndex[g, v] gives the integer index for the vertex v in the graph g.

AddEdges[g, edgeList] gives graph g with the new edges in edgeList added. edgeList can have the form {a, b} to add a single edge {a, b} or the form {{a, b}, {c, d}, ...}, to ...