For a digraph $G=(V,E)$ with vertices $i$ and $j$, let $P_ij$ represent a directed $ij$ path. Then the graph$$
R = \left(V\left(G\right),\left\{\left(i,j\right):i,j \in V\left(G\right), P_{ij} \in G\right\}\right)$$
is said to be the reachability graph of $G$, and the adjacency matrix of $R$ is said to be $G$'s reachability matrix. (Note that when $G$ is undirected, we simply take each undirected edge to be bidirectional.) Vertices which are adjacent in the reachability graph are connected by one or more directed paths in the original graph; thus, structural equivalence classes in the reachability graph are synonymous with strongly connected components in the original structure.
Bear in mind that -- as with all matters involving connectedness -- reachability is strongly related to size and density. Since, for any given density, almost all structures of sufficiently large size are connected, reachability graphs associated with large structures will generally be complete. Measures based on the reachability graph, then, will tend to become degenerate in the large $|V(G)|$ limit (assuming constant positive density).