Identifying influential nodes in a network is a fundamental issue due to its wide applications, such as accelerating information diffusion or halting virus spreading. Many measures based on the network topology have emerged over the years to identify influential nodes such as Betweenness, Closeness, and Eigenvalue centrality. However, although most real-world networks are modular, few measures exploit this property. Recent works have shown that it has a significant effect on the dynamics on networks. In a modular network, a node has two types of influence: a local influence (on the nodes of its community) through its intra-community links and a global influence (on the nodes in other communities) through its inter-community links. Depending of the strength of the community structure, these two components are more or less influential. Based on this idea, we propose to extend all the standard centrality measures defined for networks with no community structure to modular networks. The so-called "Modular centrality" is a two dimensional vector. Its first component quantifies the local influence of a node in its community while the second component quantifies its global influence on the other communities of the network. In order to illustrate the effectiveness of the Modular centrality extensions, comparison with their scalar counterpart are performed in an epidemic process setting. Simulation results using the Susceptible-Infected-Recovered (SIR) model on synthetic networks with controlled community structure allows getting a clear idea about the relation between the strength of the community structure and the major type of influence (global local). Furthermore, experiments on real-world networks demonstrate the merit of this approach.
proposed a variation of the K-shell decomposition for modular networks @cite_0 . They suggest that the intra-community and the inter-community links should be considered separately in the K-core decomposition process. Their method works as follows: (i) After the removal of nodes with intra-community links, the K-shell decomposition of the remaining nodes is computed. It is associated with an index of @math . (ii) After the removal of nodes with inter-community links, the K-shell of the remaining nodes is computed. It is associated with an index of @math . (iii) A new measure is then calculated and assigned to each node based on the linear combination of both @math and @math in order to find nodes that are at the same time bridges and hubs located in the core of the network. Experiments have been performed using SIR simulations on Facebook friendship networks at US Universities. Results show that this strategy is more efficient than the classical K-shell decomposition, the Degree and the Betweenness centrality measures.
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An efficient strategy for the identification of influential spreaders that could be used to control epidemics within populations would be of considerable importance. Generally, populations are characterized by its community structures and by the heterogeneous distributions of weak ties among nodes bridging over communities. A strategy for community networks capable of identifying influential spreaders that accelerate the spread of disease is here proposed. In this strategy, influential spreaders serve as target nodes. This is based on the idea that, in k-shell decomposition, weak ties and strong ties are processed separately. The strategy was used on empirical networks constructed from online social networks, and results indicated that this strategy is more accurate than other strategies. Its effectiveness stems from the patterns of connectivity among neighbors, and it successfully identified the important nodes. In addition, the performance of the strategy remained robust even when there were errors in the structure of the network.