How is this type of digraph called?

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Suppose $G=(V,E)$ is a digraph, then we can construct a graph $G'=(V',E')$, where $V'=V$ and $E'$ are defined with the property that $(a,b)\in E'$ iff there exists a path from node $a$ to $b$. What is this type of graph called? What are some of its properties?

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If you do this, you will get a complete (in both directions) digraph on each strongly connected component (SCC), and then between every pair of SCCs you will either have no edges, or all edges in one direction. If you contract each SCC to a single vertex, you get something that resembles the condensation of the digraph, but it won't normally be exactly the same. This is because the condensation includes an edge only where two SCCs are connected by a single edge, whereas your definition puts edges whenever there is a directed path between the SCCs, which may need to go through another SCC. So what you have would be the transitive closure of the condensation; I don't think there is a specific name for that.