On the largest strong components in \(m\)-out digraphs (Q1182737)

For \(n>m\geq 2\), the author considers the digraph \(D(m,n)\) obtained by randomly choosing a digraph from the set of all \(m\)-out digraphs (every vertex has an outdegree equal to \(m)\). For a fixed \(m\geq 2\), almost every \(D(m,n)\) has a unique largest strongly connected subdigraph \(S\). Let \(N(m,n)\) denote the number of the vertices of this subdigraph \(S\). Then \(n^{-1}\cdot N(m,n)\) converges in probability to \(1-y(m)\) where \(y(m)\) is the smallest root of \(y=e^{m(y-1)}\).