Conversion functions do not preserve a graph's support and vertex/edge decorations. That is, the resulting graph has standard support and no vertex/edge decorations. A slight exception to this rule occurs when the resulting graph is a network (of type GrphNet) and is described in detail in UnderlyingNetwork.
The rules followed in building an orientated graph from an undirected graph are the same as those described for simple graphs (see Section Converting between Graphs and Digraphs).
Given a multigraph G, produce a multidigraph 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]. If G has a loop at u, then D will have a directed loop at u.
Given a multidigraph G with edge-set E, produce a multidigraph D whose vertex-set is the same as that of G and whose edge-set is { [u, v] : [v, u] ∈E }.
Any simple (di)graph can be converted into a multi(di)graph and any multi(di)graph can be converted into a simple (di)graph. The resulting graph has standard support and neither vertex labels nor edge decorations, unless it is a network, in which case all the edges in the resulting graph are assigned a capacity of 1 (0 if loops).
Let G be a graph and e an edge of G from u to v and let H be the graph resulting from the conversion. If G and H are both undirected or both directed then e is also an edge of H. If G is undirected while H is undirected then both edges [u, v] and [v, u] are edges of H. If G is directed while H is directed then the edge {u, v} is an edge of H.
Since these conversion functions do not retain the original graph's support and vertex/edge decorations, they may also be used when requiring a copy of a graph G without G's support and vertex/edge decorations.
The underlying simple graph of the graph G. The support and vertex/edge decorations of G are not retained.
The underlying simple digraph of the graph G. The support and vertex/edge decorations of G are not retained.
The underlying multigraph of the graph G. The support and vertex/edge decorations of G are not retained.
The underlying multidigraph of the graph G. The support and vertex/edge decorations of G are not retained.
The underlying network of the graph G. The support and vertex/edge decorations of G are not retained except when G is a network in which case only the edge capacities are retained. If G is not a network, then all the edge capacities are set to 1 (0 for loops).