Identifying influential nodes using overlapping modularity vitality

Abstract

It is of paramount importance to uncover influential nodes to control diffusion phenomena in a network. In recent works, there is a growing trend to investigate the role of the community structure to solve this issue. Up to now, the vast majority of the so-called community-aware centrality measures rely on non-overlapping community structure. However, in many real-world networks, such as social networks, the communities overlap. In other words, a node can belong to multiple communities. To overcome this drawback, we propose and investigate the "Overlapping Modularity Vitality" centrality measure. This extension of "Modularity Vitality" quantifies the community structure strength variation when removing a node. It allows identifying a node as a hub or a bridge based on its contribution to the overlapping modularity of a network. A comparative analysis with its non-overlapping version using the Susceptible-Infected-Recovered (SIR) epidemic diffusion model has been performed on a set of six real-world networks. Overall, Overlapping Modularity Vitality outperforms its alternative. These results illustrate the importance of incorporating knowledge about the overlapping community structure to identify influential nodes effectively. Moreover, one can use multiple ranking strategies as the two measures are signed. Results show that selecting the nodes with the top positive or the top absolute centrality values is more effective than choosing the ones with the maximum negative values to spread the epidemic.

Map equation centrality: community-aware centrality based on the map equation

“…Depending on whether deleting a node and its incident links increases or decreases the partitions modularity, the result can be positive or negative. Following previous evaluations, we consider modularity vitality's absolute value (Rajeh et al 2021). Community hub-bridge determines a node u's importance by considering its intra-and inter-community links, weighing them by u's own community size and the number of other communities it links to, respectively, assigning high importance to nodes with many links in large communities and nodes with many links to a large number…”

“…The second spreading process we use to evaluate map equation centrality's performance is a discrete-time SIR disease spreading simulation. We follow the approach taken by Rajeh et al (2021) to test how accurately the centrality measures identify influential nodes.…”

“…To address this issue, network scientists have developed community-aware centrality scores that typically define node importance in terms of intra-community and inter-community link patterns. They commonly evaluate their effectiveness in a disease spreading setting where the objective is to contain an epidemic by immunising a limited fraction of the population (Cherifi et al 2019;Masuda 2009;Rajeh et al 2021). For example, community-based betweenness centrality considers only shortest paths with endpoints in different communities (Kitromilidis and Evans 2018).…”

“…Overlapping modular centrality generalises modular centrality and takes into account the possibly multiple community memberships that nodes have, resulting in increased influence in the local parts of a network . Recently, modularity vitality has been proposed (Magelinski et al 2021) based on the community-detection approach known as modularity (Newman and Girvan 2004) and generalised to overlapping communities (Rajeh et al 2021).…”

“…To evaluate the performance of map equation centrality, we apply it to twelve empirical networks to identify influential nodes. Like in previous work on centrality scores, we contrast our predictions with the spreading power of nodes obtained from simulations of a Susceptible-Infected-Recovered (SIR) disease-spreading model Rajeh et al 2021) and the adoptions of ideas modelled by the linear threshold model (Rajeh et al 2022). For comparison, we include degree centrality as a local measure, betweenness centrality as a global measure, as well as three other community-aware centrality measures in our evaluation.…”