Each digraph G V E has an associated undirected graph G VE

Each digraph G = (V, E) has an associated (undirected) graph G\' = (V\',E\') where V\' = V and each directed edge (M,V) epsilon becomes an (undirected) edges

Solution

By definition

A simple graph, , is an unweighted, undirected graph containing no graph loops or multiple edges

With this definition , G\' (the associated undirected graph to G) need not be simple.

Consider G to have two vertices a and b, one directed edge from a to b and another from b to a.

Then G\' has multiple edges between a and b, and hence not simple