The model networks show a peak* in the modularity for an average degree close to the World Airline Network. This peak is due to the increase in coreness of the network as the core collapses and a larger core takes shape (see Fig. 5—local peak** observed in the distribution of coreness for modelled networks). For the same average degree, L/N=5.6, the model generates many interconnected modules while the World Airline Network shows little or no links between modules. Different colours represent different communities and the size of the nodes classify them into core (large) or periphery (small). Data for system sizes N=200, 400 and 1,000 are averages over 100 realizations.