Identifying influential spreaders in networks is an essential issue in order to prevent epidemic spreading, or to accelerate information diffusion. Several centrality measures take advantage of various network topological properties to quantify the notion of influence. However, the vast majority of works ignore its community structure while it is one of the main features of many real-world networks. In a recent study, we show that the centrality of a node in a network with non-overlapping communities depends on two features: Its local influence on the nodes belonging to its community, and its global influence on the nodes belonging to the other communities. Using global and local connectivity of the nodes, we introduced a framework allowing to redefine all the classical centrality measures (designed for networks without community structure) to non-overlapping modular networks. In this paper, we extend the so-called “Modular Centrality” to networks with overlapping communities. Indeed, it is a frequent scenario in real-world networks, especially for social networks where nodes usually belong to several communities. The “Overlapping Modular Centrality” is a two-dimensional measure that quantifies the local and global influence of overlapping and non-overlapping nodes. Extensive experiments have been performed on synthetic and real-world data using the Susceptible-Infected-Recovered (SIR) epidemic model. Results show that the Overlapping Modular Centrality outperforms its alternatives designed for non-modular networks. These investigations provide better knowledge on the influence of the various parameters governing the overlapping community structure on the nodes’ centrality. Additionally, two combinations of the components of the Overlapping Modular Centrality are evaluated. Comparative analysis with competing methods shows that they produce more efficient centrality scores.

Although community structure is ubiquitous in complex networks, few works exploit this topological property to control epidemics. In this work, devoted to networks with non-overlapping community structure (i.e, a node belongs to a single community), we propose and investigate three deterministic immunization strategies. In order to characterize the influence of a node, various pieces of information are used such as the number of communities that the node can reach in one hop, the nature of the links (intra community links, inter community links), the size of the communities, and the interconnection density between communities. Numerical simulations with the Susceptible-Infected-Removed (SIR) epidemiological model are conducted on both real-world and synthetic networks. Experimental results show that the proposed strategies are more effective than classical deterministic alternatives that are agnostic of the community structure. Additionally, they outperform stochastic and deterministic strategies designed for modular networks.

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 intercommunity 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