WeightedAdjacencyGraph[wmat] gives the graph with weighted adjacency matrix wmat.WeightedAdjacencyGraph[{v_1, v_2, ...}, wmat] gives the graph with vertices v_i and weighted ...
IncidenceGraph[m] gives the graph with incidence matrix m.
PropertyValue[{obj, item}, name] gives the property value associated with name for item in obj.
BarabasiAlbertGraphDistribution[n, k] represents a Barabasi\[Dash]Albert graph distribution for n-vertex graphs where a new vertex with k edges is added at each step.
FindHamiltonianCycle[g] finds a Hamiltonian cycle in the graph g if one exists.
GraphEdit[] opens an interactive graph editor.GraphEdit[g] plots the graph g in the interactive graph editor.
GraphDistanceMatrix[g] gives a matrix in which the (i, j)\[Null]^th entry is the length of a shortest path in g between vertices i and j.GraphDistanceMatrix[g, Parent] ...
TreePlot[{v i 1 -> v j 1, v i 2 -> v j 2, ...}] generates a tree plot of the graph in which vertex v_ik is connected to vertex v_jk.TreePlot[{{v i 1 -> v j 1, lbl_1}, ...}] ...
TreeGraph[{v_1, v_2, ...}, {u_1, u_2, ...}] yields a tree where u_i is the predecessor of v_i.TreeGraph[{e_1, e_2, ...}] yields a tree with edges e_j.TreeGraph[{v_1, v_2, ...
MinCut
(Graph Utilities Package Symbol) MinCut[g, k] partitions the undirected graph g into k parts where the number of edge cuts is approximately minimized.