Expected number of directed links in a network

Question

Suppose we have a network with n nodes, in which every directed link exists with probability p (independent from each other). What would be the expected number of directed links if we express them in n and p? For example E(p,n) = ...?

Answer 1

Let $L(n)$ be the number of all possible links on the network with $n$ nodes (this is either $n^2$ or $n^2 - n$ depending on whether you allow a node to be incident to itself or not). In the situation you describe you have $L(n)$ independent Bernoulli distributions each with parameter $p$ and are asking for the expected total number of successes, that is, you are actually looking at a binomial distribution with parameters $L(n)$ and $p$ and asking for the expected value of it, which is $p L(n)$.