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

TL;DR

HawkesRank introduces a dynamic, event-driven centrality measure based on multivariate Hawkes processes, enabling real-time importance ranking that adapts to shocks and outperforms static metrics in online communication analysis.

Contribution

The paper presents HawkesRank, a novel framework that models influence using Hawkes processes, connecting classical centrality measures to a dynamic, observable activity-based importance metric.

Findings

HawkesRank closely tracks system activity in simulations and real data.

It outperforms static centrality metrics in predicting importance.

Classical indices like Katz and PageRank are special cases of the framework.

Abstract

Quantifying influence in networks is important across science, economics, and public health, yet widely used centrality measures remain limited: they rely on static representations, heuristic network constructions, and purely endogenous notions of importance, while offering little semantic connection to observable activity. We introduce HawkesRank, a dynamic framework grounded in multivariate Hawkes point processes that models exogenous drivers (intrinsic contributions) and endogenous amplification (self- and cross-excitation). This yields a principled, empirically calibrated, and adaptive importance measure. Classical indices such as Katz centrality and PageRank emerge as mean-field limits of the framework, clarifying both their validity and their limitations. Unlike static averages, HawkesRank measures importance through instantaneous event intensities, enabling prediction, transparent endo-exo decomposition, and adaptability to shocks. Using both simulations and empirical analysis of emotion dynamics in online communication platforms, we show that HawkesRank closely tracks system activity and consistently outperforms static centrality metrics.