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Traditional measures\u2014such as mutual information (MI), interaction information (II), the redundancy-synergy index (RSI), and O-information (OI)\u2014are typically limited to static analyses not accounting for temporal correlations and become computationally unfeasible in large networks due to the exponential growth of the number of interactions to be analyzed. To address these challenges, first a framework is introduced to extend these information-theoretic measures to dynamic processes. This includes the II rate (IIR), RSI rate (RSIR), and the OI rate gradient (\u0394OIR), enabling the dynamic analysis of HOIs. Moreover, a stepwise strategy identifying groups of nodes (multiplets) that maximize either redundant or synergistic HOIs is devised, offering deeper insights into complex interdependencies. The framework is validated through simulations of networks composed of cascade, common drive, and common target mechanisms, modelled using vector autoregressive (VAR) processes. The feasibility of the proposed approach is demonstrated through its application in climatology, specifically by analyzing the relationships between climate variables that govern El Ni\u00f1o and the Southern Oscillation (ENSO) using historical climate data.<\/jats:p>","DOI":"10.3390\/math13132081","type":"journal-article","created":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T09:24:18Z","timestamp":1750757058000},"page":"2081","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Information-Theoretic Sequential Framework to Elicit Dynamic High-Order Interactions in High-Dimensional Network Processes"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0455-6466","authenticated-orcid":false,"given":"Helder","family":"Pinto","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica da Universidade do Porto (CMUP), Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, 4169-007 Porto, Portugal"},{"name":"Intelligent Systems Associate Laboratory (LASI), Centro Algoritmi, University of Minho, 4804-533 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6956-6323","authenticated-orcid":false,"given":"Yuri","family":"Antonacci","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Palermo, 90128 Palermo, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7409-8130","authenticated-orcid":false,"given":"Gorana","family":"Mijatovic","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8969-9257","authenticated-orcid":false,"given":"Laura","family":"Sparacino","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Palermo, 90128 Palermo, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5873-8564","authenticated-orcid":false,"given":"Sebastiano","family":"Stramaglia","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Bari Aldo Moro, and INFN Sezione di Bari, 70126 Bari, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3271-5348","authenticated-orcid":false,"given":"Luca","family":"Faes","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Palermo, 90128 Palermo, Italy"},{"name":"Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3218-7001","authenticated-orcid":false,"given":"Ana Paula","family":"Rocha","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica da Universidade do Porto (CMUP), Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, 4169-007 Porto, Portugal"},{"name":"Intelligent Systems Associate Laboratory (LASI), Centro Algoritmi, University of Minho, 4804-533 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1038\/ncomms1705","article-title":"Network physiology reveals relations between network topology and physiological function","volume":"3","author":"Bashan","year":"2012","journal-title":"Nat. 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