HawkesRank: Event-driven centrality for real-time importance ranking.

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 show that influence can instead be interpreted through multivariate Hawkes point processes that model exogenous drivers and endogenous amplification (self- and cross-excitation). This yields a principled, empirically calibrated, and adaptive notion of importance grounded in observable event dynamics. Classical indices such as Katz centrality and PageRank emerge as stationary mean-field limits of this formulation, clarifying both their interpretation and their limitations. Unlike static averages, the resulting rankings are determined by instantaneous event intensities, allowing rankings to adapt to shocks while distinguishing endogenous amplification from exogenous activity. Using both simulations and empirical analysis of emotion dynamics in online communication platforms, we show that this event-driven formulation captures temporally evolving system activity more effectively than static centrality metrics.