# Converting between Graphs and Digraphs

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.

## `OrientatedGraph(G): GrphUnd -> GrphDir`

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 $\{ u,v\rbrace$, 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.

## `UnderlyingGraph(D): Grph -> GrphUnd`

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.

## `UnderlyingDigraph(G): Grph -> GrphDir`

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.