HawkesRank: Event-Driven Centrality for Real-Time Importance Ranking

A team led by renowned complexity scientist Didier Sornette has published HawkesRank, a new mathematical framework for measuring influence in dynamic networks. Published on arXiv, the research addresses fundamental limitations in traditional centrality measures like PageRank and Katz centrality, which rely on static network snapshots and heuristic constructions. HawkesRank instead uses multivariate Hawkes point processes—a statistical model for event sequences—to quantify importance through real-time event intensities. This allows the model to distinguish between intrinsic contributions (exogenous drivers) and network amplification effects (endogenous excitation), providing a transparent decomposition of influence sources.

The framework's key innovation is its dynamic, event-driven nature. While classical centrality measures emerge as mean-field limits of HawkesRank, the new model continuously adapts to new data, enabling real-time ranking and prediction of future activity. In empirical tests analyzing emotion dynamics on online communication platforms, HawkesRank consistently outperformed static metrics by more closely tracking actual system activity. The model proved particularly effective at adapting to external shocks and identifying nodes whose importance changes rapidly based on real-world events.

From a technical perspective, HawkesRank represents a significant advancement in network science methodology. By grounding centrality measurement in empirically calibrated point processes, it moves beyond heuristic approaches to a principled statistical framework. The 10-page paper with 8 pages of supplementary material demonstrates how the model can be applied to diverse domains including social networks, economic systems, and public health monitoring, where understanding real-time influence dynamics is critical.