HararyGraph (Built-in Mathematica Symbol)

HararyGraph[k, n] generates the minimal k-connected graph on n vertices H k, n.

PathGraph (Built-in Mathematica Symbol)

PathGraph[{v_1, v_2, ...}] yields a path with vertices v_i and edges between v_i and v i +\[ThinSpace]1 .PathGraph[{e_1, e_2, ...}] yields a path with edges ...

VertexOutDegree (Built-in Mathematica Symbol)

VertexOutDegree[g] gives the list of vertex out-degrees for all vertices in the graph g.VertexOutDegree[g, v] gives the vertex out-degree for the vertex v.

IncidenceGraph (Built-in Mathematica Symbol)

IncidenceGraph[m] gives the graph with incidence matrix m.

PetersenGraph (Built-in Mathematica Symbol)

PetersenGraph[n, k] gives the generalized Petersen graph P n, k.

WeightedAdjacencyGraph (Built-in Mathematica Symbol)

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 ...

ConnectedComponents (Built-in Mathematica Symbol)

ConnectedComponents[g] gives the connected components of the graph g.ConnectedComponents[g, {v_1, v_2, ...}] gives the connected components that include at least one of the ...

DepthFirstScan (Built-in Mathematica Symbol)

DepthFirstScan[g, s, {"event_1" -> f_1, "event_2" -> f_2, ...}] performs a depth-first scan of the graph g starting at the vertex s and evaluates f_i whenever "event_i" ...

FindGraphIsomorphism (Built-in Mathematica Symbol)

FindGraphIsomorphism[g_1, g_2] finds an isomorphism that maps the graph g_1 to g_2 by renaming vertices.

AdjacencyGraph (Built-in Mathematica Symbol)

AdjacencyGraph[amat] gives the graph with adjacency matrix amat.AdjacencyGraph[{v_1, v_2, ...}, amat] gives the graph with vertices v_i and adjacency matrix amat.