Consider a random directed graph with $n$ nodes. Each node has on average $x$ number of incoming edges.
How many nodes are not part of a cycle? Alternatively phrased, how many strongly connected components are a singleton?
I would think that this question has been answered in the literature. Versions of it have been answered on this site (see here for a solution for bipartite graphs in which each node has a unique incoming edge expected number of cycles in a "random" bipartite directed graph).
I would be very grateful if anyone could provide me with a reference.
Simulations with $x=\log(n)$ show that the fraction of such nodes becomes smaller as $n$ grows, dropping from 68% with $n=25$ to 40% with $n=500$.
