Centrality measures for networks with community structure

Understanding the network structure, and finding out the influential nodes is a challenging issue in large networks. Identifying the most influential nodes in a network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is being done to devise centrality measures which could efficiently identify the most influential nodes in a network. There are two major approaches to this problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology, while on the other end, random strategies are completely agnostic about the network structure. Centrality measures that can deal with a limited knowledge of the network structure are of prime importance. Indeed, in practice, information about the global structure of the overall network is rarely available or hard to acquire. Even if available, the structure of the network might be too large that it is too much computationally expensive to calculate global centrality measures. To that end, a centrality measure is proposed here that requires information only at the community level. Indeed, most of the real-world networks exhibit a community structure that can be exploited efficiently to discover the influential nodes. We performed a comparative evaluation of prominent global deterministic strategies together with stochastic strategies, an available and the proposed deterministic community-based strategy. Effectiveness of the proposed method is evaluated by performing experiments on synthetic and real-world networks with community structure in the case of immunization of nodes for epidemic control.