Consider a graph $G$ of $N$ vertices and $M$ edges, and assume $G$ has typical complex network properties: it is not necessarily connected, but it has a high clustering coefficient and a giant connected component with low average distance.

Now, consider a graph $G'$ defined as the sub-graph of $G$ induced by a randomly chosen set of $n$ vertices. Let us denote by $m$ its number of edges.

• Is $G'$ likely to have the typical properties of an Erdős–Rényi random graph?

• What is the expected value of $m$?

Thank you.