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 when model networks present absent or low modular structure ID strategy is more effective than IB to decrease the LCC. Conversely, in the case the model network present higher modularity, the IB strategy becomes the most effective to fragment the LCC. In addition, networks with higher modularity present a signature of a 1st order percolation transition and a decrease of the LCC with one or several abrupt changes when nodes are removed, for both strategies; differently, networks with non-modular structure or low modularity show a 2nd order percolation transition networks when nodes are removed. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the network 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 for both the node attack strategies, especially for the IB 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 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.
Highlights
The study of real-world complex networks has attracted much attention in recent decades because a large number of complex systems in the real-world can be considered as complex networks, such as social (Borgatti et al 2009; Bellingeri et al 2020a, 2020b), technological (Albert et al 1999; Faloutsos et al 1999), biological (Jeong et al 2000; Barra and Agliari 2010), ecological complex systems (Bellingeri and Bodini 2013; Bellingeri and Vincenzi 2013)
Robustness of non‐modular scale‐free BA network In Fig. 3 we depict the outcome of a scale-free BA network of size N = 10,000 nodes and average degree k = 4 without rewiring process subjected to initial degree (ID) and initial betweenneess (IB) attack strategies
We found that the 1st largest connected component (LCC) decreases continuously under both strategies and the network is completely broken down at a critical occupation probability pc (0.62 and 0.56 for ID and IB, respectively)
Summary
The study of real-world complex networks has attracted much attention in recent decades because a large number of complex systems in the real-world can be considered as complex networks, such as social (Borgatti et al 2009; Bellingeri et al 2020a, 2020b), technological (Albert et al 1999; Faloutsos et al 1999), biological (Jeong et al 2000; Barra and Agliari 2010), ecological complex systems (Bellingeri and Bodini 2013; Bellingeri and Vincenzi 2013). Many real-world networks show a scale-free structure, making them resilient to random node failure (Cohen et al 2000) but can disintegrate quickly when a small proportion of important nodes are removed (Albert et al 1999). The network’s robustness, which evaluates the capability of network to hold its functioning under such failures or attacks has drawn extensive attention in recent years (Albert and Barabási 2002; Cohen et al 2000; Callaway et al 2000; Iyer et al 2013; Bellingeri et al 2015; Bellingeri et al 2014; Dall’Asta et al 2006; Nguyen and Nguyen 2018; Wandelt et al 2018; Bellingeri et al 2019, 2020a, 2020b). In social contact network on which a disease can spread, it is critical to understand how node removal through vaccination affects the spread of the disease to efficiently prevent an epidemic (Holme 2004; Wang et al 2015; Bellingeri et al 2020a, 2020b)
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