The current implementation of the Erdos-Renyi graph seems to have an issue related to the generation of the adjacency matrix. In particular, the edge probability does not follow the input probability p but it is roughly half. This is due to the following lines:

G.W = sprandsym(N,p)>0;
G.W(1:N 1:end) = 0;

where sprandsym(N,p) generates a sparse matrix with nonzero probability p but the nonzero entries are normally distributed, so taking >0 only selects half of those.

A quick fix, albeit inefficient, is

G.W = tril(rand(N,N)<p);
G.W = G.W - eye(N);
G.W = G.W G.W';