Figure 1: Percolation diagrams of real networks.

(a) We consider the graph corresponding to the giant component of the peer-to-peer Gnutella network as of August 31, 2002 (refs 32, 33). The black thin line represents the site percolation order parameter S as a function of the site occupation probability p. We calculate also the order parameter B for bond percolation and multiply it by p to obtain the red dashed line. The average clustering coefficient of the network is C=0.0055. Such a low value indicates that the tree-like approximation holds with sufficient accuracy for this network. We further estimated the error V of the law S=pB, by considering the integral . We find V=0.0002. (b) We consider the graph corresponding to the giant component of the Internet at the autonomous system level in the period January 2004 to November 2007 (ref. 34). The description of the various curves is identical to those appearing in panel a. The clustering coefficient for this network is C=0.2082. The error associated to equation (5) is V=0.0016.