  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, 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 the 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.
