Suppose you have several random graphs. Each one has $n$ nodes, connected among them with probability $p$. There are $r$ random graphs.
Now, each node is connected to nodes of another random graph with probability $q$, in general different from $p$. 
Suppose that any node is a friend of anybody to whom he is either directly connected to by an edge, or by anyone with whom they share an endnode, i.e. anyone with whom there exists a path of length at most 2.

First question: How many friends each node has in expectation?

Second question: now suppose that half nodes in each graph are men, half women. How many expected women friends each male node has?

The answer must be a generalization of this one: 
[Probability of friendship](https://math.stackexchange.com/questions/2773550/probability-of-friendship?noredirect=1#comment5719830_2773550)

Furthermore, the probability that node x is not a friend of someone in his own graph is something like 

$(1-p) \sum^n\_k \sum^{r(n-1)}\_h p^k q^h (1-p)^{n-k} (1-q)^{(r-1)n-h} (1-p)^{k} (1-q)^{h}$

and the probability that node x is not a friend of someone in a different graph is something like

$(1-q) \sum^n\_k \sum^{r(n-1)}\_h p^k q^h (1-p)^{n-k} (1-q)^{(r-1)n-h} (1-p)^{k} (1-q)^{h}$

but in both cases I am missing a combinatorial factor.