Influence-Spreading Model reveals gaps in standard network centrality metrics

A new arXiv paper (2608.18797) from researchers at Finland's National Defence University and Aalto University evaluates whether classic network centrality measures can capture probabilistic influence flows. The team's Influence-Spreading Model (ISM) defines three measures: out-centrality (average probability a node influences others), in-centrality (average probability others influence a node), and ISM betweenness (change in total influence when a node is removed). Unlike traditional metrics, ISM accounts for edge transmission probabilities and walks up to a specified maximum length.

Testing against 4 real-world online social networks and 9 synthetic networks (Erdős-Rényi, navigable small-world, and directed scale-free) with edge probabilities drawn from three beta distributions, the authors found strong Pearson and Spearman correlations between ISM out-centrality and weighted out-degree plus outward Katz centrality—especially at low edge probabilities. However, in-centrality correlations varied wildly by topology, sometimes turning negative, while ISM betweenness diverged from shortest-path betweenness as alternative influence paths became relevant. The practical takeaway: standard centrality measures are fine for approximating broadcasting influence but systematically miss the nuances of who receives influence and who serves as a probabilistic intermediary.