Note that the two functions UnderlyingGraph and UnderlyingDigraph may also be used when one needs to get a copy of a graph G without G's support and vertex/edge decorations.
Given a graph G, produce a digraph D whose vertex-set is the same as that of G and whose edge-set consists of the edges of G, each given a direction. The edges of D are always directed from the lower numbered vertex to the higher numbered vertex. Thus, if G contains the edge { u, v }, then D will have the edge [u, v] if u < v, otherwise the edge [u, v]. The support and vertex/edge decorations of G are not retained.
The underlying graph G of the graph D; G has the same vertex-set as D. If D is undirected, then G is a copy of D without D's support and vertex/edge decorations. If D is directed, then two vertices u and v are adjacent in G if and only if, in D, there is either an edge directed from u to v or from v to u. The support and vertex/edge decorations of G are not retained.
The underlying digraph D of the graph G; D has the same vertex-set as G. If G is directed, then D is a copy of G without D's support and vertex/edge decorations. If G is undirected, then if vertices u and v are adjacent in G then, in D, there will be both an edge directed from u to v and an edge directed from v to u. The support and vertex/edge decorations of G are not retained.