Strongly Connected Component

We can define a binary relation $\sim \subseteq V\times V$ on the set of vertices such that:

$$u\sim v⟺u=v\text{ or there is a path }u⇝v\text{ and a path }v⇝u$$

A strongly connected component is therefor a maximal subset $C\subseteq V$ such that $u\sim v$ for all $u,v\in C$.