{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T10:17:06Z","timestamp":1786184226944,"version":"3.56.0"},"reference-count":53,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T00:00:00Z","timestamp":1582675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1447634"],"award-info":[{"award-number":["IIS-1447634"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Contagion models are a primary lens through which we understand the spread of information over social networks. However, simple contagion models cannot reproduce the complex features observed in real-world data, leading to research on more complicated complex contagion models. A noted feature of complex contagion is social reinforcement that individuals require multiple exposures to information before they begin to spread it themselves. Here we show that the quoter model, a model of the social flow of written information over a network, displays features of complex contagion, including the weakness of long ties and that increased density inhibits rather than promotes information flow. Interestingly, the quoter model exhibits these features despite having no explicit social reinforcement mechanism, unlike complex contagion models. Our results highlight the need to complement contagion models with an information-theoretic view of information spreading to better understand how network properties affect information flow and what are the most necessary ingredients when modeling social behavior.<\/jats:p>","DOI":"10.3390\/e22030265","type":"journal-article","created":{"date-parts":[[2020,2,27]],"date-time":"2020-02-27T03:21:16Z","timestamp":1582773676000},"page":"265","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Complex Contagion Features without Social Reinforcement in a Model of Social Information Flow"],"prefix":"10.3390","volume":"22","author":[{"given":"Tyson","family":"Pond","sequence":"first","affiliation":[{"name":"Department of Mathematics &amp; Statistics, University of Vermont, Burlington, VT 05405, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saranzaya","family":"Magsarjav","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2740-9829","authenticated-orcid":false,"given":"Tobin","family":"South","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8191-1997","authenticated-orcid":false,"given":"Lewis","family":"Mitchell","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4614-0792","authenticated-orcid":false,"given":"James P.","family":"Bagrow","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, University of Vermont, Burlington, VT 05405, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1126\/science.1167742","article-title":"SOCIAL SCIENCE: Computational Social Science","volume":"323","author":"Lazer","year":"2009","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Tumasjan, A., Sprenger, T.O., Sandner, P.G., and Welpe, I.M. (2010, January 23\u201326). Predicting elections with twitter: What 140 characters reveal about political sentiment. Proceedings of the Fourth International AAAI Conference on Weblogs and Social Media, Washington, DC, USA.","DOI":"10.1609\/icwsm.v4i1.14009"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Conover, M.D., Ferrara, E., Menczer, F., and Flammini, A. (2013). The Digital Evolution of Occupy Wall Street. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0064679"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Castells, M. (2015). Networks of Outrage and Hope: Social Movements in the Internet Age, John Wiley & Sons.","DOI":"10.7312\/blau17412-091"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1126\/science.1256297","article-title":"Unique in the shopping mall: On the reidentifiability of credit card metadata","volume":"347","author":"Radaelli","year":"2015","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e1701172","DOI":"10.1126\/sciadv.1701172","article-title":"Leaking privacy and shadow profiles in online social networks","volume":"3","author":"Garcia","year":"2017","journal-title":"Sci. Adv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","article-title":"Measuring Information Transfer","volume":"85","author":"Schreiber","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.physd.2013.07.001","article-title":"Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings","volume":"267","author":"Sun","year":"2014","journal-title":"Phys. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e1501158","DOI":"10.1126\/sciadv.1501158","article-title":"The dynamics of information-driven coordination phenomena: A transfer entropy analysis","volume":"2","author":"Perra","year":"2016","journal-title":"Sci. Adv."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, D., Wen, Z., Tong, H., Lin, C.Y., Song, C., and Barab\u00e1si, A.L. (April, January 28). Information spreading in context. Proceedings of the 20th international conference on World wide web (WWW 2011), Hyderabad, India.","DOI":"10.1145\/1963405.1963508"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1038\/s41562-018-0510-5","article-title":"Information flow reveals prediction limits in online social activity","volume":"3","author":"Bagrow","year":"2019","journal-title":"Nat. Hum. Behav."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"075304","DOI":"10.1063\/1.5011403","article-title":"The quoter model: A paradigmatic model of the social flow of written information","volume":"28","author":"Bagrow","year":"2018","journal-title":"Chaos"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1126\/science.1185231","article-title":"The Spread of Behavior in an Online Social Network Experiment","volume":"329","author":"Centola","year":"2010","journal-title":"Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1093\/comnet\/cnt006","article-title":"Cascading behaviour in complex socio-technical networks","volume":"1","author":"Banos","year":"2013","journal-title":"J. Complex Netw."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1002\/j.1538-7305.1951.tb01366.x","article-title":"Prediction and Entropy of Printed English","volume":"30","author":"Shannon","year":"1951","journal-title":"Bell Labs Tech. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1109\/18.669425","article-title":"Nonparametric entropy estimation for stationary processes and random fields, with applications to English text","volume":"44","author":"Kontoyiannis","year":"1998","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1126\/science.1177170","article-title":"Limits of Predictability in Human Mobility","volume":"327","author":"Song","year":"2010","journal-title":"Science"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ziv, J., and Merhav, N. (1993, January 17\u201322). A Measure of Relative Entropy between Individual Sequences with Application to Universal Classification. Proceedings of the IEEE International Symposium on Information Theory, San Antonio, TX, USA.","DOI":"10.1109\/18.243444"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1137\/140956166","article-title":"Causal Network Inference by Optimal Causation Entropy","volume":"14","author":"Sun","year":"2015","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"ref_20","unstructured":"Cover, T.M., and Thomas, J.A. (1991). Elements of Information Theory, John Wiley & Sons, Inc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1086\/226707","article-title":"Threshold Models of Collective Behavior","volume":"83","author":"Granovetter","year":"1978","journal-title":"Am. J. Sociol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5766","DOI":"10.1073\/pnas.082090499","article-title":"A simple model of global cascades on random networks","volume":"99","author":"Watts","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.physa.2006.06.018","article-title":"Cascade dynamics of complex propagation","volume":"374","author":"Centola","year":"2007","journal-title":"Phys. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5962","DOI":"10.1073\/pnas.1116502109","article-title":"Structural diversity in social contagion","volume":"109","author":"Ugander","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"020901","DOI":"10.1103\/PhysRevE.80.020901","article-title":"Percolation and epidemics in random clustered networks","volume":"80","author":"Miller","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1103\/RevModPhys.87.925","article-title":"Epidemic processes in complex networks","volume":"87","author":"Castellano","year":"2015","journal-title":"Rev. Mod. Phys."},{"key":"ref_27","first-page":"71","article-title":"Mathematical modeling of complex contagion on clustered networks","volume":"3","author":"Fennell","year":"2015","journal-title":"Front. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Gray, C., Mitchell, L., and Roughan, M. (2018, January 23\u201327). Super-blockers and the effect of network structure on information cascades. Proceedings of the Companion Proceedings of the The Web Conference 2018, Lyon, France.","DOI":"10.1145\/3184558.3191590"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1086\/521848","article-title":"Complex Contagions and the Weakness of Long Ties","volume":"113","author":"Centola","year":"2007","journal-title":"Am. J. Sociol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Granovetter, M.S. (1977). The Strength of Weak Ties. Social Networks, Elsevier.","DOI":"10.1016\/B978-0-12-442450-0.50025-0"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1731","DOI":"10.21105\/joss.01731","article-title":"EoN (Epidemics on Networks): A fast, flexible Python package for simulation, analytic approximation, and analysis of epidemics on networks","volume":"4","author":"Miller","year":"2019","journal-title":"J. Open Source Softw."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"68002","DOI":"10.1209\/0295-5075\/78\/68002","article-title":"How does degree heterogeneity affect an order-disorder transition?","volume":"78","author":"Lambiotte","year":"2007","journal-title":"Europhys. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2330","DOI":"10.1038\/srep02330","article-title":"Threshold-limited spreading in social networks with multiple initiators","volume":"3","author":"Singh","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_35","unstructured":"Milo, R., Kashtan, N., Itzkovitz, S., Newman, M.E., and Alon, U. (2003). On the uniform generation of random graphs with prescribed degree sequences. arXiv."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1080\/15427951.2010.557277","article-title":"A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees","volume":"6","author":"Blitzstein","year":"2011","journal-title":"Internet Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"026113","DOI":"10.1103\/PhysRevE.69.026113","article-title":"Finding and evaluating community structure in networks","volume":"69","author":"Newman","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"P09008","DOI":"10.1088\/1742-5468\/2005\/09\/P09008","article-title":"Comparing community structure identification","volume":"2005","author":"Danon","year":"2005","journal-title":"J. Stat. Mech."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"016107","DOI":"10.1103\/PhysRevE.83.016107","article-title":"Stochastic blockmodels and community structure in networks","volume":"83","author":"Karrer","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"P10008","DOI":"10.1088\/1742-5468\/2008\/10\/P10008","article-title":"Fast unfolding of communities in large networks","volume":"2008","author":"Blondel","year":"2008","journal-title":"J. Stat. Mech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"013046","DOI":"10.1103\/PhysRevResearch.2.013046","article-title":"Impact of the distribution of recovery rates on disease spreading in complex networks","volume":"2","author":"Petri","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"088701","DOI":"10.1103\/PhysRevLett.113.088701","article-title":"Erratum: Optimal Network Modularity for Information Diffusion","volume":"113","author":"Nematzadeh","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_43","first-page":"2018","article-title":"The Colorado index of complex networks","volume":"20","author":"Clauset","year":"2016","journal-title":"Retrieved July"},{"key":"ref_44","unstructured":"Knuth, D.E. (1993). Stanford GraphBase: A platform for Combinatorial Computing, Addison-Wesley."},{"key":"ref_45","unstructured":"Faulkner, R.R. (1983). Music on Demand: Composers and Careers in the Hollywood Film Industry, Transaction Books."},{"key":"ref_46","unstructured":"Freeman, S.C., and Freeman, L.C. (1979). The Networkers Network: A Study of the Impact of a New Communications Medium on Sociometric Structure, University of California."},{"key":"ref_47","unstructured":"Sampson, S.F. (1968). A novitiate in a Period of Change: An Experimental and Case Study of Social Relationships. [Ph.D. Thesis, Cornell University]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1137\/16M1066142","article-title":"Eigenvector-Based Centrality Measures for Temporal Networks","volume":"15","author":"Taylor","year":"2017","journal-title":"Multiscale Model. Simul."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"43","DOI":"10.5210\/fm.v7i4.941","article-title":"Uncloaking Terrorist Networks","volume":"7","author":"Krebs","year":"2002","journal-title":"First Monday"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1086\/228667","article-title":"Social Contagion and Innovation: Cohesion versus Structural Equivalence","volume":"92","author":"Burt","year":"1987","journal-title":"Am. J. Sociol."},{"key":"ref_51","unstructured":"Kapferer, B. (1972). Strategy and Transaction in an African Factory: African Workers and Indian Management in a Zambian Town, Manchester University Press."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1007\/s00265-003-0651-y","article-title":"The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations","volume":"54","author":"Lusseau","year":"2003","journal-title":"Behav. Ecol. Sociobiol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"065103","DOI":"10.1103\/PhysRevE.68.065103","article-title":"Self-similar community structure in a network of human interactions","volume":"68","author":"Danon","year":"2003","journal-title":"Phys. Rev. E"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/265\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:02:00Z","timestamp":1760173320000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/265"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,26]]},"references-count":53,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["e22030265"],"URL":"https:\/\/doi.org\/10.3390\/e22030265","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,26]]}}}