I have a undirected random graph with node degree distribution $P(k)$, I pick a random vertex $v_0$ and I randomly select a neighbor $v_1$ (the selection is made with uniform probability).
What is the probability that v1 has at least $1$ neighbor which is not a neighbor of $v_0$?
Another formulation of the question: if the expected node degree of v1 is $
Thanks
Michele