Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

TL;DR

This study examines how network modularity influences the robustness of both model and real-world social networks under degree and betweenness-based node attacks, revealing that higher modularity generally increases fragility.

Contribution

It introduces a new method to generate modular networks and systematically analyzes the impact of modularity on network robustness and attack strategy effectiveness.

Findings

Higher modularity decreases network robustness under attack.

Degree-based attack is more effective on low-modularity networks.

Betweenness-based attack is more effective on high-modularity networks.

Abstract

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.