The volume of the giant component of a random graph with given expected degrees

We consider the random graph model G(w) for a given expected degree sequence w = (w(1), w(2),..., w(n)). If the expected average degree is strictly greater than 1, then almost surely the giant component in G of G( w) has volume ( i.e., sum of weights of vertices in the giant component) equal to lambda(0)Vol(G) + O(root n log(3.5) n), where lambda(0) is the unique nonzero root of the equation Sigma(n)(i-1) w(i)e(-wi lambda) = (1-lambda) Sigma(n)(i=1) w(i), and where Vol(G) = Sigma(i) w(i).