  In this paper we investigate how the modularity of model and real-world
social networks affect their robustness and the efficacy of node attack
(removal) strategies based on node degree (ID) and node betweenness (IB). We
build Barabasi-Albert model networks with different modularity by a new ad hoc
algorithm that rewire links forming networks with community structure. We
traced the network robustness using the largest connected component (LCC). We
find that higher level of modularity decreases the model network robustness
under both attack strategies, i.e. model network with higher community
structure showed faster LCC disruption when subjected to node removal. Very
interesting, we find that when model networks showed non-modular structure or
low modularity, the degree-based (ID) is more effective than the
betweenness-based node attack strategy (IB). Conversely, in the case the model
network present higher modularity, the IB strategies becomes clearly the most
effective to fragment the LCC. Last, we investigated how the modularity of the
network structure evaluated by the modularity indicator (Q) affect the
robustness and the efficacy of the attack strategies in 12 real-world social
networks. We found that the modularity Q is negatively correlated with the
robustness of the real-world social networks under IB node attack strategy
(p-value< 0.001). This result indicates how real-world networks with higher
modularity (i.e. with higher community structure) may be more fragile to
betwenness-based node attack. The results presented in this paper unveil the
role of modularity and community structure for the robustness of networks and
may be useful to select the best node attack strategies in network.
