Importance of overlapping network nodes in influence spreading

In complex networks, “circles” are attribute-defined subgraphs whose nodes share common characteristics (e.g., group membership or categories). Nodes that belong to multiple such circles form overlapping regions, but their role in influence spreading processes remains somewhat underexplored. We analyse several networks with circle structures using a probabilistic influence spreading model for processes of simple and complex contagion in them. We quantify the importance of these overlapping nodes using three metrics, i.e., In-Centrality, Out-Centrality, and Betweenness Centrality, which represent the susceptibility, spreading power, and mediating role of nodes, respectively. We find that, at each stage of the spreading process, the overlapping nodes systematically exhibit greater influence than the non-overlapping nodes, even when accounting for structural heterogeneity, i.e., node connectivity. Furthermore, we observe that the criteria used to define circles shape the overlapping effects. When we restrict our analysis to only the largest circles, we find that circles reflect not only node-level attributes but also of topological importance. These findings help clarify the distinction between local attribute-driven circles and global community structures, thus highlighting the strategic importance of overlapping nodes in spreading dynamics. This provides a foundation for future research on overlapping nodes in both circles and communities.