GraphComplement[g] gives the graph complement of the graph g.
EdgeRules[g] gives the list of edge rules for the graph g.
GXL
(Mathematica Import/Export Format) GXL graph data format. Used for the storage and exchange of graphs. GXL is an acronym derived from Graph Exchange Language. XML-based format. Represents typed, attributed, ...
VertexCoordinates is an option to Graph and related functions that specifies the coordinates to use to place the center of vertices.
GraphDisjointUnion[g_1, g_2] gives the graph disjoint union of the graphs g_1 and g_2.GraphDisjointUnion[g_1, g_2, ...] gives the disjoint union of g_1, g_2, ....
GraphDifference[g_1, g_2] gives the graph difference of the graphs g_1 and g_2.
UndirectedGraphQ[g] yields True if the graph g is an undirected graph and False otherwise.
BooleanGraph[bfunc, g_1, ..., g_n] gives the Boolean graph defined by the Boolean function bfunc on the graphs g_1, ..., g_n.
GraphIntersection[g_1, g_2] gives the graph intersection of the graphs g_1 and g_2.GraphIntersection[g_1, g_2, ...] gives the graph intersection of g_1, g_2, ....
CompleteGraphQ[g] yields True if the graph g is a complete graph, and False otherwise.CompleteGraphQ[g, vlist] yields True if the subgraph induced by vlist is a complete ...