I'm interested in the statistics of strongly connected components in random directed graphs. However, I'm unable to find any results on this, partly because I don't know the terminology to search for.

By "random directed graph" I mean a digraph with $N$ nodes, where every possible edge has a uniform probability $p$ of being included in the graph, independently of the other edges. For undirected graphs this is sometimes known (possibly erroneously) as the Erdös-Rényi model, but for digraphs I don't know the correct term.

Equivalently, given a random (in general non-symmetric) matrix where every element has an independent probability of being non-zero, one can do a change of basis using a permutation matrix to put it in block upper triangular form; I'm interested in the statistics of the number and size of the resulting blocks on the diagonal.

I'm most interested in knowing the expected number of strongly connected components of size $>1$, for a given $N$ and $p$, but any results concerning the statistics of the strongly connected components (e.g. the size of the largest one) would be enormously helpful. I'm interested primarily in the limit of large $N$, for non-extreme values of $p$.

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