Figure 2

Modular random graphs with n =150, m =375, K =3, P ( s =50)=1 and p _k is power law with modularity values of: a) Q =0.1; b) Q = 0.3; and c) Q = 0.6. As the modularity increases, the ratio of the total number of edges within modules to the number of edges in the network increases (i.e. $\overline{d_w}$ increases), while the remaining parameter values (degree distribution, network mean degree, number of modules) are held constant.