{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T05:48:51Z","timestamp":1724737731522},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T00:00:00Z","timestamp":1699401600000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,11,7]]},"abstract":"Abstract<\/jats:title>\n Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this article, we extend the multi-type branching process method developed in Keating et al., (2022), which relies on networks having homogenous node properties, to a more general class of clustered networks. Using a model of socially inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique-cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.<\/jats:p>","DOI":"10.1093\/comnet\/cnad042","type":"journal-article","created":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T21:10:45Z","timestamp":1697145045000},"source":"Crossref","is-referenced-by-count":2,"title":["A generating-function approach to modelling complex contagion on clustered networks with multi-type branching processes"],"prefix":"10.1093","volume":"11","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-6911-7432","authenticated-orcid":false,"given":"Leah A","family":"Keating","sequence":"first","affiliation":[{"name":"MACSI, Department of Mathematics and Statistics, University of Limerick , Limerick V94 T9PX, Ireland"},{"name":"Department of Mathematics, University of California , Los Angeles, CA 90095, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-3410-2817","authenticated-orcid":false,"given":"James P","family":"Gleeson","sequence":"additional","affiliation":[{"name":"MACSI, Department of Mathematics and Statistics, University of Limerick , Limerick V94 T9PX, Ireland"}]},{"given":"David J P","family":"O\u2019Sullivan","sequence":"additional","affiliation":[{"name":"MACSI, Department of Mathematics and Statistics, University of Limerick , Limerick V94 T9PX, Ireland"}]}],"member":"286","published-online":{"date-parts":[[2023,11,8]]},"reference":[{"key":"2023111007021587300_cnad042-B1","doi-asserted-by":"crossref","first-page":"036122","DOI":"10.1103\/PhysRevE.68.036122","article-title":"Why social networks are different from other types of networks","volume":"68","author":"Newman","year":"2003","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B2","doi-asserted-by":"crossref","volume-title":"Dynamical Systems on Networks: A Tutorial","author":"Porter","year":"2016","DOI":"10.1007\/978-3-319-26641-1"},{"key":"2023111007021587300_cnad042-B3","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":"2023111007021587300_cnad042-B4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep02522","article-title":"Virality prediction and community structure in social networks","volume":"3","author":"Weng","year":"2013","journal-title":"Sci. Rep"},{"key":"2023111007021587300_cnad042-B5","first-page":"021004","article-title":"Binary-state dynamics on complex networks: pair approximation and beyond","volume":"3","author":"Gleeson","year":"2013","journal-title":"Phys. Rev. X"},{"key":"2023111007021587300_cnad042-B6","first-page":"1","article-title":"Branching process descriptions of information cascades on Twitter","volume":"8","author":"Gleeson","year":"2021","journal-title":"J. Complex Netw"},{"key":"2023111007021587300_cnad042-B7","doi-asserted-by":"crossref","first-page":"036112","DOI":"10.1103\/PhysRevE.83.036112","article-title":"The unreasonable effectiveness of tree-based theory for networks with clustering","volume":"83","author":"Melnik","year":"2011","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B8","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":"2023111007021587300_cnad042-B9","doi-asserted-by":"crossref","first-page":"20140694","DOI":"10.1098\/rsif.2014.0694","article-title":"Complex contagion process in spreading of online innovation","volume":"11","author":"Karsai","year":"2014","journal-title":"J. R. Soc. Interface"},{"key":"2023111007021587300_cnad042-B10","doi-asserted-by":"crossref","first-page":"e0184148","DOI":"10.1371\/journal.pone.0184148","article-title":"Evidence of complex contagion of information in social media: an experiment using Twitter bots","volume":"12","author":"Monsted","year":"2017","journal-title":"PLoS One"},{"key":"2023111007021587300_cnad042-B11","first-page":"695","author":"Romero","year":"2011"},{"key":"2023111007021587300_cnad042-B12","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1371\/journal.pone.0180802","article-title":"Evidence for complex contagion models of social contagion from observational data","volume":"12","author":"Sprague","year":"2017","journal-title":"PLoS One"},{"key":"2023111007021587300_cnad042-B13","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.ecocom.2005.04.005","article-title":"The impacts of network topology on disease spread","volume":"2","author":"Shirley","year":"2005","journal-title":"Ecol. Complex"},{"key":"2023111007021587300_cnad042-B14","first-page":"71","article-title":"Mathematical modeling of complex contagion on clustered networks","volume":"3","author":"O\u2019Sullivan","year":"2015","journal-title":"Front. Phys"},{"key":"2023111007021587300_cnad042-B15","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":"2023111007021587300_cnad042-B16","doi-asserted-by":"crossref","first-page":"0343306","DOI":"10.1103\/PhysRevE.105.034306","article-title":"Multitype branching process method for modeling complex contagion on clustered networks","volume":"105","author":"Keating","year":"2022","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B17","first-page":"137","author":"Kempe","year":"2003"},{"key":"2023111007021587300_cnad042-B18","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1186\/s13174-017-0066-z","article-title":"Generative models of online discussion threads: state of the art and research challenges","volume":"8","author":"Arag\u00f3n","year":"2017","journal-title":"J. Internet Serv. Appl"},{"key":"2023111007021587300_cnad042-B19","doi-asserted-by":"crossref","first-page":"10411","DOI":"10.1073\/pnas.1313895111","article-title":"A simple generative model of collective online behavior","volume":"111","author":"Gleeson","year":"2014","journal-title":"Proc. Natl. Acad. Sci"},{"issue":"1","key":"2023111007021587300_cnad042-B20","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1038\/s41467-017-01212-0","article-title":"Temporal profiles of avalanches on networks","volume":"8","author":"Gleeson","year":"2017","journal-title":"Nat. Commun"},{"key":"2023111007021587300_cnad042-B21","first-page":"021019","article-title":"Effects of network structure, competition and memory time on social spreading phenomena","volume":"6","author":"Gleeson","year":"2016","journal-title":"Phys. Rev. X"},{"key":"2023111007021587300_cnad042-B22","doi-asserted-by":"crossref","first-page":"048701","DOI":"10.1103\/PhysRevLett.112.048701","article-title":"Competition-induced criticality in a model of meme popularity","volume":"112","author":"Gleeson","year":"2014","journal-title":"Phys. Rev. Lett"},{"key":"2023111007021587300_cnad042-B23","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1017\/nws.2020.33","article-title":"Single-seed cascades on clustered networks","volume":"9","author":"McSweeney","year":"2020","journal-title":"Netw. Sci"},{"key":"2023111007021587300_cnad042-B24","doi-asserted-by":"crossref","first-page":"066114","DOI":"10.1103\/PhysRevE.74.066114","article-title":"Spreading dynamics on heterogeneous populations: multitype network approach","volume":"74","author":"Vazquez","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B25","doi-asserted-by":"crossref","first-page":"L030301","DOI":"10.1103\/PhysRevE.103.L030301","article-title":"Multitype branching and graph product theory of infectious disease outbreaks","volume":"103","author":"Vazquez","year":"2021","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B26","volume-title":"Matrix Population Models","author":"Caswell","year":"2018"},{"key":"2023111007021587300_cnad042-B27","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1287\/mnsc.2015.2158","article-title":"The structural virality of online diffusion","volume":"62","author":"Goel","year":"2016","journal-title":"Manag. Sci"},{"key":"2023111007021587300_cnad042-B28","doi-asserted-by":"crossref","first-page":"062311","DOI":"10.1103\/PhysRevE.101.062311","article-title":"Quantifying uncertainty in a predictive model for popularity dynamics","volume":"101","author":"O\u2019Brien","year":"2020","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B29","doi-asserted-by":"crossref","first-page":"058701","DOI":"10.1103\/PhysRevLett.103.058701","article-title":"Random graphs with clustering","volume":"103","author":"Newman","year":"2009","journal-title":"Phys. Rev. Lett"},{"key":"2023111007021587300_cnad042-B30","doi-asserted-by":"crossref","first-page":"020901","DOI":"10.1103\/PhysRevE.80.020901","article-title":"Percolation and epidemics in random clustered networks","volume":"83","author":"Miller","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B31","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1093\/imamat\/22.3.275","article-title":"On the fast Fourier transform inversion of probability generating functions","volume":"22","author":"Cavers","year":"1978","journal-title":"IMA J. Appl. Math"},{"key":"2023111007021587300_cnad042-B32","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1073\/pnas.1110586109","article-title":"Suppressing cascades of load in interdependent networks","volume":"109","author":"Brummitt","year":"2012","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"2023111007021587300_cnad042-B33","first-page":"P07028","article-title":"Exact solution of a two-type branching process: clone size distribution in cell division kinetics","volume":"1","author":"Antal","year":"2010","journal-title":"J. Stat. Mech"},{"key":"2023111007021587300_cnad042-B34","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1038\/s42005-021-00618-z","article-title":"Network clique cover approximation to analyze complex contagions through group interactions","volume":"4","author":"Burgio","year":"2021","journal-title":"Commun Phys"},{"key":"2023111007021587300_cnad042-B35","doi-asserted-by":"crossref","first-page":"044314","DOI":"10.1103\/PhysRevE.105.044314","article-title":"Degree correlations in graphs with clique clustering","volume":"105","author":"Mann","year":"2022","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B36","doi-asserted-by":"crossref","first-page":"036104","DOI":"10.1103\/PhysRevE.74.036104","article-title":"Finding community structure in networks using the eigenvectors of matrices","volume":"74","author":"Newman","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B37","doi-asserted-by":"crossref","first-page":"027104","DOI":"10.1103\/PhysRevE.72.027104","article-title":"Community detection in complex networks using extremal optimization","volume":"72","author":"Duch","year":"2005","journal-title":"Phys. Rev. E"},{"key":"2023111007021587300_cnad042-B38","author":"Mann","year":"2022"}],"container-title":["Journal of Complex Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/11\/6\/cnad042\/53028774\/cnad042.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/11\/6\/cnad042\/53028774\/cnad042.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T07:02:48Z","timestamp":1699599768000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comnet\/article\/doi\/10.1093\/comnet\/cnad042\/7380485"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,7]]},"references-count":38,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,11,7]]}},"URL":"https:\/\/doi.org\/10.1093\/comnet\/cnad042","relation":{},"ISSN":["2051-1329"],"issn-type":[{"value":"2051-1329","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,12,1]]},"published":{"date-parts":[[2023,11,7]]}}}