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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.<\/jats:p>","DOI":"10.1093\/pnasnexus\/pgag292","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T08:08:56Z","timestamp":1788250136000},"source":"Crossref","is-referenced-by-count":0,"title":["HawkesRank: Event-driven centrality for real-time importance ranking"],"prefix":"10.1093","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7874-7962","authenticated-orcid":false,"given":"Didier","family":"Sornette","sequence":"first","affiliation":[{"name":"Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology , Shenzhen 518055 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-4511-9812","authenticated-orcid":false,"given":"Yishan","family":"Luo","sequence":"additional","affiliation":[{"name":"Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology , Shenzhen 518055 ,","place":["China"]},{"name":"Warwick Business School, University of Warwick , Coventry CV4 7AL ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1359-565X","authenticated-orcid":false,"given":"Sandro Claudio","family":"Lera","sequence":"additional","affiliation":[{"name":"Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology , Shenzhen 518055 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,9,1]]},"reference":[{"key":"2026091009063219600_pgag292-B1","first-page":"187","article-title":"Designing organizations for an information-rich world","volume":"70","author":"Simon","year":"1996","journal-title":"Int Libr Crit Writings Econ"},{"key":"2026091009063219600_pgag292-B2","doi-asserted-by":"crossref","first-page":"E4512","DOI":"10.1073\/pnas.1419828112","article-title":"The search engine manipulation effect (SEME) and its possible impact on the outcomes of elections","volume":"112","author":"Epstein","year":"2015","journal-title":"Proc Natl Acad Sci U S A"},{"key":"2026091009063219600_pgag292-B3","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0169-7552(98)00110-X","article-title":"The anatomy of a large-scale hypertextual web search engine","volume":"30","author":"Brin","year":"1998","journal-title":"Comput Netw ISDN Syst"},{"key":"2026091009063219600_pgag292-B4","doi-asserted-by":"crossref","first-page":"10570","DOI":"10.1073\/pnas.0900943106","article-title":"The building blocks of economic complexity","volume":"106","author":"Hidalgo","year":"2009","journal-title":"Proc Natl Acad Sci U S A"},{"key":"2026091009063219600_pgag292-B5","doi-asserted-by":"crossref","first-page":"4300","DOI":"10.1093\/rfs\/hhab133","article-title":"Competition links and stock returns","volume":"35","author":"Eisdorfer","year":"2022","journal-title":"Rev Financ Stud"},{"key":"2026091009063219600_pgag292-B6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep00541","article-title":"Debtrank: too central to fail? 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