Strongly connected component graph (directed graph)

Let $G = (V,E)$ be a directed graph. Suppose $G$ has strongly connected components $S = \{S_1, \ldots, S_n\}$. We can define the strongly connected component graph as a directed graph with vertices $S$ and edges

$$E' =\{(S_i, S_j) \vert \ s_i \in S_i, s_j \in S_j\ \mbox{ with } (s_i, s_j) \in E\}.$$