EigenvectorCentrality[g] gives a list of eigenvector centralities for the vertices in the graph g.EigenvectorCentrality[g, "In"] gives a list of in-centralities for a ...

FindEulerianCycle[g] finds an Eulerian cycle in the graph g if one exists.FindEulerianCycle[g, k] finds at most k Eulerian cycles.

PlanarGraphPlot[{{x_1, y_1}, {x_2, y_2}, ...}] plots the Delaunay triangulation of the points {{x_1, y_1}, ...}.PlanarGraphPlot[{{x_1, y_1}, {x_2, y_2}, ...}, g] plots the ...

CoxeterGraph gives a non-Hamiltonian graph with a high degree of symmetry such that there is a graph automorphism taking any path of length 3 to any other.

ThomassenGraph returns a hypotraceable graph, a graph G that has no Hamiltonian path but whose subgraph G - v for every vertex v has a Hamiltonian path.

PageRanks[g] give the page rank of the graph g as a rule list.

MinimumBandwidthOrdering[g] attempts to find a vertex ordering that minimizes the bandwidth of the undirected graph g.MinimumBandwidthOrdering[m] attempts to find row and ...

ClosenessCentrality[g] gives a list of closeness centralities for the vertices in the graph g.

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.

BrelazColoring[g] returns a vertex coloring in which vertices are greedily colored with the smallest available color in decreasing order of vertex degree.