GraphComplement[g] gives the complement of graph g.

GraphDifference[g, h] constructs the graph resulting from subtracting the edges of graph h from the edges of graph g.

GraphicQ[s] yields True if the list of integers s is a graphic sequence, and thus represents a degree sequence of some graph.

GraphIntersection[g_1, g_2, ...] constructs the graph defined by the edges that are in all the graphs g_1, g_2, ....

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 ...

Graph[e, v, opts] represents a graph object where e is the list of edges annotated with graphics options, v is a list of vertices annotated with graphics options, and opts is ...

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 ...

GraphPolynomial[n, x] returns a polynomial in x in which the coefficient of x^m is the number of nonisomorphic graphs with n vertices and m edges. GraphPolynomial[n, x, ...

GraphPower[g, k] gives the k\[Null]^th power of graph g. This is the graph whose vertex set is identical to the vertex set of g and that contains an edge between vertices i ...

GraphProduct[g_1, g_2, ...] constructs the product of graphs g_1, g_2, and so forth.