Immunization of networks with community structure

In this study, an efficient method to immunize modular networks (i.e. networks with community structure) is proposed. The immunization of networks aims at fragmenting networks into small parts with a small number of removed nodes. Its applications include prevention of epidemic spreading, protection against intentional attacks on networks, and conservation of ecosystems. Although preferential immunization of hubs is efficient, good immunization strategies for modular networks have not been established. On the basis of an immunization strategy based on eigenvector centrality, we develop an analytical framework for immunizing modular networks. To this end, we quantify the contribution of each node to the connectivity in a coarse-grained network among modules. We verify the effectiveness of the proposed method by applying it to model and real networks with modular structure.