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Our main tools come from mean theory and graph theory. The case, when the root set of the network (influencers, news agencies, etc.) is ergodic is fully discussed. The other possibility, when the root contains more than one component, is partially discussed and it could be a motivation for further research.<\/jats:p>","DOI":"10.1017\/nws.2025.10012","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T09:31:06Z","timestamp":1762162266000},"source":"Crossref","is-referenced-by-count":0,"title":["A nonlinear model of evolution of beliefs in social networks"],"prefix":"10.1017","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-8924-7449","authenticated-orcid":false,"given":"P\u00e1l","family":"Burai","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02w42ss30","id-type":"ROR","asserted-by":"publisher"}],"name":"Budapest University of Technology and Economics"}]},{"given":"Pawe\u0142","family":"Pasteczka","sequence":"additional","affiliation":[{"name":"University of Rzesz\u00f3w"}]}],"member":"56","published-online":{"date-parts":[[2025,11,3]]},"reference":[{"key":"S205012422510012X_ref16","doi-asserted-by":"publisher","DOI":"10.7153\/mia-2021-24-15"},{"key":"S205012422510012X_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-023-01922-6"},{"key":"S205012422510012X_ref19","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1961.11.1529"},{"key":"S205012422510012X_ref5","first-page":"267","article-title":"Sulle medie multiple di potenze","volume":"5","author":"Bonferroni","year":"1950","journal-title":"Bollett. dell\u2019Unione Mat. 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