{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:29:20Z","timestamp":1787228960895,"version":"build-2736575974"},"reference-count":51,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1922952"],"award-info":[{"award-number":["1922952"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:p>People's opinions evolve with time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but many social interactions in real life are polyadic (i.e., they involve three or more people). In this paper, we extend an asynchronous bounded-confidence model (BCM) on graphs, in which nodes are connected pairwise by edges, to an asynchronous BCM on hypergraphs, in which arbitrarily many nodes can be connected by a single hyperedge. We show that our hypergraph BCM converges to consensus for a wide range of initial conditions for the opinions of the nodes, including for nonuniform and asymmetric initial opinion distributions. We also show that, under suitable conditions, echo chambers can form on hypergraphs with community structure. We demonstrate that the opinions of nodes can sometimes jump from one opinion cluster to another in a single time step; this phenomenon (which we call \u201copinion jumping'') is not possible in standard dyadic BCMs. Additionally, we observe a phase transition in the convergence time of our BCM on a complete hypergraph when the variance $\\sigma^2$ of the initial opinion distribution equals the confidence bound $c$. We prove that the convergence time grows at least exponentially fast with the number of nodes when $\\sigma^2 &gt; c$ and the initial opinions are normally distributed. Therefore, to determine the convergence properties of our hypergraph BCM when the variance and the number of hyperedges are both large, it is necessary to use analytical methods instead of relying only on Monte Carlo simulations.<\/jats:p>","DOI":"10.1137\/21m1399427","type":"journal-article","created":{"date-parts":[[2022,1,4]],"date-time":"2022-01-04T13:33:28Z","timestamp":1641303208000},"page":"1-32","source":"Crossref","is-referenced-by-count":41,"title":["A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs"],"prefix":"10.1137","volume":"21","author":[{"given":"Abigail","family":"Hickok","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yacoub","family":"Kureh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-107X","authenticated-orcid":true,"given":"Heather Z.","family":"Brooks","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michelle","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5166-0717","authenticated-orcid":true,"given":"Mason A.","family":"Porter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,1,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2020.05.004"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(03)00171-4"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1800683115"},{"key":"atypb4","unstructured":"C. Bick, E. Gross, H. A. Harrington, and M. T. Schaub,\n                      What Are Higher-Order Networks?\n                      , preprint,arXiv:2104.11329, 2021."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/1486909"},{"key":"atypb6","unstructured":"F. Bullo,\n                      Lectures on Network Systems\n                      , Version 1.5, Kindle Direct Publishing, with contributions by Jorge Cort\u00e9s, Florian D\u00f6rfler, and Sonia Mart\u00ednez, 2021,http:\/\/motion.me.ucsb.edu\/book-lns\/."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1080\/15427951.2013.833676"},{"key":"atypb8","first-page":"35","volume":"8","author":"Cota W.","year":"2019","journal-title":"Eur. Phys. J. Sci. Data Sci."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1142\/S0219525900000078"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1974.10480137"},{"key":"atypb11","unstructured":"M. H. DeGroot and M. J. Schervish,\n                      Probability and Statistics\n                      , 4th ed., Addison-Wesley, Boston, MA, 2012."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1038\/srep37825"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(01)00574-0"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.103.012314"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1093\/poq\/nfw006"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1142\/S0129183104006728"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.09.002"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1142\/S0129183105008126"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0857"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOS1453"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.12693\/APhysPolA.127.A-55"},{"key":"atypb22","first-page":"3","volume":"5","author":"Hegselmann R.","year":"2002","journal-title":"J. Artif. Soc. Soc. Simul."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/20M1376844"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-10431-6"},{"key":"atypb25","first-page":"646","author":"Jackson M. O.","year":"2011","journal-title":"Amsterdam"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1063\/1.5017962"},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"U. Kan, M. Feng, and M. A. Porter,\n                      An Adaptive Bounded-Confidence Model of Opinion Dynamics on Networks\n                      , preprint,arXiv:2112.05856, 2021.","DOI":"10.31235\/osf.io\/gcxnf"},{"key":"atypb28","doi-asserted-by":"crossref","unstructured":"B. Klimt and Y. Yang,\n                      The Enron corpus: A new dataset for email classification research\n                      , in Machine Learning: ECML 2004, J.F. Boulicaut, F. Esposito, F. Giannotti, and D. Pedreschi, eds., Springer-Verlag, Heidelberg, Germany, 2004, pp. 217-226.","DOI":"10.1007\/978-3-540-30115-8_22"},{"key":"atypb29","unstructured":"K. Knight,\n                      Mathematical Statistics\n                      , Chapman & Hall\/CRC, Boca Raton, FL, 2000."},{"key":"atypb30","doi-asserted-by":"crossref","unstructured":"I. V. Kozitsin,\n                      Opinion dynamics of online social social network users: A micro-level analysis\n                      , J. Math. Sociol. (2021),https:\/\/doi.org\/10.1080\/0022250X.2021.1956917.","DOI":"10.1080\/0022250X.2021.1956917"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1037\/0022-3514.37.11.2098"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.02.086"},{"key":"atypb33","first-page":"1819","volume":"18","author":"Lorenz J.","year":"2007","journal-title":"Phys. A"},{"key":"atypb34","unstructured":"J. Lorenz,\n                      Repeated Averaging and Bounded Confidence: Modeling, Analysis and Simulation of Continuous Opinion Dynamics\n                      , PhD thesis, Universit\u00e4t Bremen, 2007."},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1063\/1.4790836"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.022312"},{"key":"atypb37","doi-asserted-by":"crossref","unstructured":"L. Neuh\u00e4user, R. Lambiotte, and M. T. Schaub,\n                      Consensus Dynamics and Opinion Formation on Hypergraphs\n                      , preprint,arXiv:2105.01369, 2021.","DOI":"10.1007\/978-3-030-91374-8_14"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.032310"},{"key":"atypb39","unstructured":"M. E. J. Newman,\n                      Networks\n                      , 2nd ed., Oxford University Press, Oxford, UK, 2018."},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.104.024316"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1142\/S0129183120501016"},{"key":"atypb42","first-page":"123","author":"Petty R. E.","year":"1986","journal-title":"MA"},{"key":"atypb43","first-page":"131","author":"Porter M. A.","year":"2020","journal-title":"Switzerland"},{"key":"atypb44","first-page":"1082","volume":"56","author":"Porter M. A.","year":"2009","journal-title":"Notices Amer. Math. Soc."},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1088\/2632-072X\/abcea3"},{"key":"atypb46","doi-asserted-by":"crossref","unstructured":"H. Schawe and L. Hern\u00e1ndez,\n                      Higher Order Interactions Destroy Phase Transitions in Deffuant Opinion Dynamics Model\n                      , preprint,arXiv:2111.12165, 2021.","DOI":"10.1038\/s42005-022-00807-4"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-5907.2008.00361.x"},{"key":"atypb48","doi-asserted-by":"crossref","unstructured":"L. E. Sullivan,\n                      Selective exposure\n                      , in The SAGE Glossary of the Social and Behavioral Sciences, SAGE Publishing, Thousand Oaks, CA, 2009, p. 465.","DOI":"10.4135\/9781412972024"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0157948"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2004-00126-9"},{"key":"atypb51","doi-asserted-by":"publisher","DOI":"10.1002\/cplx.10031"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1399427","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:06:43Z","timestamp":1787227603000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1399427"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,4]]},"references-count":51,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["10.1137\/21M1399427"],"URL":"https:\/\/doi.org\/10.1137\/21m1399427","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,4]]}}}