# A directed graph is semi-connected if the corresponding undirected graph is connected

The following is a problem in CLRS:

A directed graph $$G = (V, E)$$ is semiconnected if, for all pairs of vertices $$u,v in V$$,
we have $$u$$ reachable from $$v$$ or $$v$$ reachable from $$u$$. Give an efficient algorithm to determine whether
or not $$G$$ is semiconnected. Prove that your algorithm is correct, and analyze its
running time.

I know there exist correct solutions to this using topological sorting and strongly-connected components, but I had a different approach.

My approach:

Construct a new undirected graph $$G’$$, having an edge $${u,v}$$ whenever $$(u,v) in E$$ or $$(v,u) in E$$.
The graph $$G$$ is semiconnected if $$G’$$ is connected.
Will this method always be correct?