I asked this question before, but formulation was poor. I've deleted previous question and reformulate it again.
Let graph $G=(N,p)$ is finite simple incomplete directed graph of size $N$ (multiple edges and self-loops aren't allowed). Let $p$ is a probability that that for any given node $v_i$ there is an edge from this node to node $v_{k\ne i}$, $p<1$.
What is an expected numbers of cycles $<l_k>$ and closed walks $<w_k>$ of length $k$ on this graph?
Thanks!!!