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.

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 made of groups of tightly connected nodes which are sparsely connected with the rest of the network in a so-called modular structure, few measures exploit this property. Recent works have shown that it has a significant effect on the dynamics of 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 on 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 counterparts is 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.