CageGraph[k, r] gives a smallest k-regular graph of girth r for certain small values of k and r. CageGraph[r] gives CageGraph[3, r]. For k = 3, r can be 3, 4, 5, 6, 7, 8, or ...

ChangeEdges[g, e] replaces the edges of graph g with the edges in e. e can have the form {{s_1, t_1}, {s_2, t_2}, ...} or the form {{{s_1, t_1}, gr_1}, {{s_2, t_2}, gr_2}, ...

ChangeVertices[g, v] replaces the vertices of graph g with the vertices in the given list v. v can have the form {{x_1, y_1}, {x_2, y_2}, ...} or the form {{{x_1, y_1}, ...

CirculantGraph[n, l] constructs a circulant graph on n vertices, meaning the i\[Null]^th vertex is adjacent to the (i + j)\[Null]^th and (i - j)\[Null]^th vertices, for each ...

CompleteKPartiteGraph[a, b, c, ...] creates a complete k-partite graph of the prescribed shape, provided the k arguments a, b, c, ... are positive integers. An option Type ...

ConnectedQ[g] yields True if undirected graph g is connected. If g is directed, the function returns True if the underlying undirected graph is connected. ConnectedQ[g, ...

DeleteEdges[g, edgeList] gives graph g minus the list of edges edgeList. If g is undirected, then the edges in edgeList are treated as undirected edges; otherwise they are ...

DepthFirstTraversal[g, v] performs a depth-first traversal of graph g starting from vertex v, and gives a list of vertices in the order in which they were encountered. ...

DominationLattice[n] returns a Hasse diagram of the partially ordered set on integer partitions of n in which p < q if q dominates p. The function takes two options: Type and ...

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 ...