Importance of Overlapping Network Nodes in Influence Spreading

TL;DR

This study investigates the influence of overlapping nodes in complex networks, revealing their significant role in spreading processes and how circle definitions affect their impact, with implications for network influence strategies.

Contribution

The paper introduces a probabilistic influence spreading model analyzing overlapping nodes' roles, highlighting their greater influence and the impact of circle definitions on spreading dynamics.

Findings

Overlapping nodes have greater influence than non-overlapping nodes.

Circle definitions significantly shape the influence of overlapping nodes.

Overlapping nodes are crucial in both local and global spreading processes.

Abstract

In complex networks there are overlapping substructures or "circles" that consist of nodes belonging to multiple cohesive subgroups. Yet the role of these overlapping nodes in influence spreading processes remains underexplored. In the present study, we analyse networks with circle structures using a probabilistic influence spreading model for processes of simple and complex contagion. We quantify the roles of nodes using three metrics, i.e., In-Centrality, Out-Centrality, and Betweenness Centrality that represent the susceptibility, spreading power, and mediatory role of nodes, respectively, and find that at each stage of the spreading process the overlapping nodes consistently exhibit greater influence than the non-overlapping ones. Furthermore, we observe that the criteria to define circles shape the overlapping effects. When we restrict our analysis to only largest circles, we find that circles reflect not only node-level attributes but also of topological importance. These findings clarify the distinction between local attribute-driven circles and global community structures, thus highlighting the strategic importanc of overlapping nodes in spreading dynamics. This provides foundation for future research on overlapping nodes in both circles and communities.