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.
SelfLoopStyle is an option for GraphPlot and related functions that specifies how to draw self-loops that connect a vertex to itself.
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 ...
ReverseGraph[g] gives the reverse graph of the directed g.
BipartiteGraphQ[g] yields True if the graph g is a bipartite graph and False otherwise.
GraphML
(Mathematica Import/Export Format) GraphML graph data format. Standard exchange for graphs. GraphML is an acronym derived from Graph Markup Language. XML-based format. Represents typed, attributed, directed, ...
GraphUnion[g_1, g_2] gives the graph union of the graphs g_1 and g_2.GraphUnion[g_1, g_2, ...] gives the graph union of g_1, g_2, ....