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Typically, explosive synchronization occurs when the network structure is represented by the classical graph Laplacian, and the node frequency and its degree are correlated. Here, we answer the question on whether this phenomenon can be observed in networks when the oscillators are coupled via degree-biased Laplacian operators. We not only observe that this is the case but also that this new representation naturally controls the transition from explosive to standard synchronization in a network. We prove analytically that explosive synchronization emerges when using this theoretical setting in star-like networks. As soon as this star-like network is topologically converted into a network containing cycles, the explosive synchronization gives rise to classical synchronization. Finally, we hypothesize that this mechanism may play a role in switching from normal to explosive states in the brain, where explosive synchronization has been proposed to be related to some pathologies like epilepsy and fibromyalgia.<\/jats:p>","DOI":"10.1063\/5.0142418","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T13:05:39Z","timestamp":1682946339000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Topologically induced suppression of explosive synchronization"],"prefix":"10.1063","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0424-6211","authenticated-orcid":false,"given":"Manuel","family":"Miranda","sequence":"first","affiliation":[{"name":"Institute of Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC) 1 , 07122 Palma de Mallorca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4361-0576","authenticated-orcid":false,"given":"Mattia","family":"Frasca","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronics and Computer Science Engineering, University of Catania 2 , I-95125 Catania, Italy"},{"name":"Istituto di Analisi dei Sistemi ed Informatica \u201cA. 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