Counting strongly connected (k1, k2)‐directed cores
Boris G. Pittel · Random Structures and Algorithms · 2017
Consider the set of all digraphs on with M edges, whose minimum in‐degree and minimum out‐degree are at least k1 and k2 respectively. For and , we show that, among those digraphs, the fraction of k‐strongly connected digraphs is . Earlier with Dan Poole we identified a sharp edge‐density threshold for birth of a giant (k1, k2)‐core in the random digraph . Combining the claims, for with probability the giant (k1, k2)‐core exists and is k‐strongly connected.