Dijkstra[g, v] gives a shortest-path spanning tree and associated distances from vertex v of graph g. The shortest-path spanning tree is given by a list in which element i is ...

EdgeConnectivity[g] gives the minimum number of edges whose deletion from graph g disconnects it. EdgeConnectivity[g, Cut] gives a set of edges of minimum size whose deletion ...

Edges[g] gives the list of edges in g. Edges[g, All] gives the edges of g along with the graphics options associated with each edge. Edges[g, EdgeWeight] returns the list of ...

EdgeStyle is an option that allows the user to associate different sizes and shapes to edges. A line segment is the default edge. EdgeStyle can be set as part of the graph ...

GraphJoin[g_1, g_2, ...] constructs the join of graphs g_1, g_2, and so on. This is the graph obtained by adding all possible edges between different graphs to the graph ...

GraphOptions[g] returns the display options associated with g. GraphOptions[g, v] returns the display options associated with vertex v in g. GraphOptions[g, {u, v}] returns ...

HamiltonianCycle[g] finds a Hamiltonian cycle in graph g if one exists. HamiltonianCycle[g, All] gives all Hamiltonian cycles of graph g.

IncidenceMatrix[g] returns the (0, 1)-matrix of graph g, which has a row for each vertex and a column for each edge and (v, e) = 1 if and only if vertex v is incident upon ...

KSetPartitions[set, k] returns the list of set partitions of set with k blocks. KSetPartitions[n, k] returns the list of set partitions of {1, 2, ..., n} with k blocks. If ...

KSubsets[l, k] gives all subsets of set l containing exactly k elements, ordered lexicographically.