CompleteQ[g] yields True if graph g is complete. This means that between any pair of vertices there is an undirected edge or two directed edges going in opposite directions.

Diameter[g] gives the diameter of graph g, the maximum length, among all pairs of vertices in g, of a shortest path between each pair.

Distances[g, v] returns the distances in nondecreasing order from vertex v to all vertices in g, treating g as an unweighted graph.

Eccentricity[g] gives the eccentricity of each vertex v of graph g, the maximum length among all shortest paths from v.

EdgeChromaticNumber[g] gives the fewest number of colors necessary to color each edge of graph g, so that no two edges incident on the same vertex have the same color.

EdgeColoring[g] uses Brelaz's heuristic to find a good, but not necessarily minimal, edge coloring of graph g.

EquivalenceRelationQ[r] yields True if the matrix r defines an equivalence relation. EquivalenceRelationQ[g] tests whether the adjacency matrix of graph g defines an ...

FindCycle[g] finds a list of vertices that define a cycle in graph g.

GetEdgeLabels[g] returns the list of labels of the edges of g. GetEdgeLabels[g, e] returns the list of labels in graph g of the edges in e.

GetEdgeWeights[g] returns the list of weights of the edges of g. GetEdgeWeights[g, e] returns the list of weights in graph g of the edges in e.