  In this paper, we give an analytic solution for graphs with n nodes and E
edges for which the probability of obtaining a given graph G is specified in
terms of the degree sequence of G. We describe how this model naturally appears
in the context of load balancing in communication networks, namely Peer-to-Peer
overlays. We then analyse the degree distribution of such graphs and show that
the degrees are concentrated around their mean value. Finally, we derive
asymptotic results on the number of edges crossing a graph cut and use these
results $(i)$ to compute the graph expansion and conductance, and $(ii)$ to
analyse the graph resilience to random failures.
