{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T22:54:36Z","timestamp":1790808876961,"version":"4.1.0"},"reference-count":228,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T00:00:00Z","timestamp":1676851200000},"content-version":"vor","delay-in-days":1976,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Commission under the Marie Curie intra-European fellowship programme"},{"name":"Alan Turing Institute under Engineering and Physical Sciences Research Council","award":["EP\/N510129\/1"],"award-info":[{"award-number":["EP\/N510129\/1"]}]},{"name":"BNPSI Agence Nationale de la Recherche project","award":["ANR-13-BS-03-0006-01"],"award-info":[{"award-number":["ANR-13-BS-03-0006-01"]}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-12-1-0406"],"award-info":[{"award-number":["FA9550-12-1-0406"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-12-1-0453"],"award-info":[{"award-number":["FA9550-12-1-0453"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,11,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Statistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this array\u2014which can aid in modelling, computations and theoretical analysis\u2014the Aldous\u2013Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measure and appeal to the Kallenberg representation theorem for this object. We explore using completely random measures (CRMs) to define the exchangeable random measure, and we show how our CRM construction enables us to achieve sparse graphs while maintaining the attractive properties of exchangeability. We relate the sparsity of the graph to the L\u00e9vy measure defining the CRM. For a specific choice of CRM, our graphs can be tuned from dense to sparse on the basis of a single parameter. We present a scalable Hamiltonian Monte Carlo algorithm for posterior inference, which we use to analyse network properties in a range of real data sets, including networks with hundreds of thousands of nodes and millions of edges.<\/jats:p>","DOI":"10.1111\/rssb.12233","type":"journal-article","created":{"date-parts":[[2017,9,23]],"date-time":"2017-09-23T01:42:49Z","timestamp":1506130969000},"page":"1295-1366","source":"Crossref","is-referenced-by-count":105,"title":["Sparse Graphs Using Exchangeable Random Measures"],"prefix":"10.1093","volume":"79","author":[{"given":"Fran\u00e7ois","family":"Caron","sequence":"first","affiliation":[{"name":"University of Oxford , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emily B.","family":"Fox","sequence":"additional","affiliation":[{"name":"University of Washington , Seattle , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,9,23]]},"reference":[{"key":"2023022002192472200_rssb12233-cit-0001","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1214\/aoap\/1177005583","article-title":"Modelling heterogeneity in survival analysis by the compound Poisson distribution","volume":"2","author":"Aalen","year":"1992","journal-title":"Ann. Appl. Probab."},{"key":"2023022002192472200_rssb12233-cit-0002","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1145\/1134271.1134277","volume-title":"Proc. 3rd Int. Wrkshp Link Discovery","author":"Adamic","year":"2005"},{"key":"2023022002192472200_rssb12233-cit-0003","first-page":"1981","article-title":"Mixed membership stochastic blockmodels","volume":"9","author":"Airoldi","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"2023022002192472200_rssb12233-cit-0004","volume-title":"Advances in Neural Information Processing Systems","author":"Airoldi","year":"2013"},{"key":"2023022002192472200_rssb12233-cit-0005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BFb0099420","volume-title":"\u00c9cole d\u2019\u00c9t\u00e9 de Probabilit\u00e9s de Saint-Flour XIII\u20131983","author":"Aldous","year":"1985"},{"key":"2023022002192472200_rssb12233-cit-0006","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1214\/aop\/1024404421","article-title":"Brownian excursions, critical random graphs and the multiplicative coalescent","volume":"25","author":"Aldous","year":"1997","journal-title":"Ann. Probab."},{"key":"2023022002192472200_rssb12233-cit-0007","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/0047-259X(81)90099-3","article-title":"Representations for partially exchangeable arrays of random variables","volume":"11","author":"Aldous","year":"1981","journal-title":"J. Multiv. Anal."},{"key":"2023022002192472200_rssb12233-cit-0008","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1214\/aos\/1176348650","article-title":"On the bootstrap of U and V statistics","volume":"20","author":"Arcones","year":"1992","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-0009","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Barab\u00e1si","year":"1999","journal-title":"Science"},{"key":"2023022002192472200_rssb12233-cit-0010","first-page":"361","article-title":"Gephi: an open source software for exploring and manipulating networks","author":"Bastian","year":"2009","journal-title":"Proc. 3rd Int. Conf. Weblogs and Social Media"},{"key":"2023022002192472200_rssb12233-cit-0011","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/12-AOP755","article-title":"Asymptotic behavior and distributional limits of preferential attachment graphs","volume":"42","author":"Berger","year":"2014","journal-title":"Ann. Probab."},{"key":"2023022002192472200_rssb12233-cit-0012","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511617768","volume-title":"Random Fragmentation and Coagulation Processes","author":"Bertoin","year":"2006"},{"key":"2023022002192472200_rssb12233-cit-0013","doi-asserted-by":"crossref","first-page":"21068","DOI":"10.1073\/pnas.0907096106","article-title":"A nonparametric view of network models and Newman\u2013Girvan and other modularities","volume":"106","author":"Bickel","year":"2009","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023022002192472200_rssb12233-cit-0014","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1214\/11-AOS904","article-title":"The method of moments and degree distributions for network models","volume":"39","author":"Bickel","year":"2011","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-0015","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1214\/aos\/1176342372","article-title":"Ferguson distributions via P\u00f3lya urn schemes","volume":"1","author":"Blackwell","year":"1973","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-0016","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0195-6698(80)80030-8","article-title":"A probabilistic proof of an asymptotic formula for the number of labelled regular graphs","volume":"1","author":"Bollob\u00e1s","year":"1980","journal-title":"Eur. J. Combin."},{"key":"2023022002192472200_rssb12233-cit-0017","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511814068","volume-title":"Random Graphs","author":"Bollob\u00e1s","year":"2001"},{"key":"2023022002192472200_rssb12233-cit-0018","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/rsa.20168","article-title":"The phase transition in inhomogeneous random graphs","volume":"31","author":"Bollob\u00e1s","year":"2007","journal-title":"Rand. Struct. Algs"},{"key":"2023022002192472200_rssb12233-cit-0019","first-page":"211","volume-title":"Surveys in Combinatorics","author":"Bollob\u00e1s","year":"2009"},{"key":"2023022002192472200_rssb12233-cit-0020","volume-title":"Sparse exchangeable graphs and their limits via graphon processes","author":"Borgs","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-0021","volume-title":"An Lp theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions","author":"Borgs","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-0022","volume-title":"An Lp theory of sparse graph convergence II: LD convergence, quotients, and right convergence","author":"Borgs","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-0023","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1002\/rsa.20694","article-title":"Convergent sequences of sparse graphs: a large deviations approach","volume":"51","author":"Borgs","year":"2017","journal-title":"Rand. Struct. Algs"},{"key":"2023022002192472200_rssb12233-cit-0024","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1007\/s00039-010-0044-0","article-title":"Moments of two-variable functions and the uniqueness of graph limits","volume":"19","author":"Borgs","year":"2010","journal-title":"Geometr. Functnl Anal."},{"key":"2023022002192472200_rssb12233-cit-0025","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1016\/j.aim.2008.07.008","article-title":"Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing","volume":"219","author":"Borgs","year":"2008","journal-title":"Adv. Math."},{"key":"2023022002192472200_rssb12233-cit-0026","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1007\/s10955-006-9168-x","article-title":"Generating simple random graphs with prescribed degree distribution","volume":"124","author":"Britton","year":"2006","journal-title":"J. Statist. Phys."},{"key":"2023022002192472200_rssb12233-cit-0027","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1239\/aap\/1029955251","article-title":"Generalized gamma measures and shot-noise Cox processes","volume":"31","author":"Brix","year":"1999","journal-title":"Adv. Appl. Probab."},{"key":"2023022002192472200_rssb12233-cit-0028","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1080\/10618600.1998.10474787","article-title":"General methods for monitoring convergence of iterative simulations","volume":"7","author":"Brooks","year":"1998","journal-title":"J. Computnl Graph. Statist."},{"key":"2023022002192472200_rssb12233-cit-0029","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1093\/nar\/gkg340","article-title":"Topological structure analysis of the protein\u2013protein interaction network in budding yeast","volume":"31","author":"Bu","year":"2003","journal-title":"Nucleic Acids Res."},{"key":"2023022002192472200_rssb12233-cit-0030","volume-title":"Austauschbare stochastische Variablen und ihre Grenzwerts\u00e4tze","author":"B\u00fchlmann","year":"1960"},{"key":"2023022002192472200_rssb12233-cit-0031","volume-title":"Advances in Neural Information Processing Systems","author":"Caron","year":"2012"},{"key":"2023022002192472200_rssb12233-cit-0032","volume-title":"Bayesian nonparametric models of sparse and exchangeable random graphs","author":"Caron","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-0033","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1214\/14-AOAS717","article-title":"Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes","volume":"8","author":"Caron","year":"2014","journal-title":"Ann. Appl. Statist."},{"key":"2023022002192472200_rssb12233-cit-0034","first-page":"1683","article-title":"Stochastic gradient Hamiltonian Monte Carlo","volume":"32","author":"Chen","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"2023022002192472200_rssb12233-cit-0035","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1214\/13-AOS1173","article-title":"Co-clustering separately exchangeable network data","volume":"42","author":"Choi","year":"2014","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-0036","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1137\/070710111","article-title":"Power-law distributions in empirical data","volume":"51","author":"Clauset","year":"2009","journal-title":"SIAM Rev."},{"key":"2023022002192472200_rssb12233-cit-0037","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1038\/nphys560","article-title":"Reaction\u2013diffusion processes and metapopulation models in heterogeneous networks","volume":"3","author":"Colizza","year":"2007","journal-title":"Nat. Phys."},{"key":"2023022002192472200_rssb12233-cit-0038","volume-title":"An Introduction to the Theory of Point Processes","author":"Daley","year":"2003"},{"key":"2023022002192472200_rssb12233-cit-0039","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-49835-5","volume-title":"An Introduction to the Theory of Point Processes","author":"Daley","year":"2008"},{"key":"2023022002192472200_rssb12233-cit-0040","first-page":"18","article-title":"Random variate generation for exponentially and polynomially tilted stable distributions","volume":"19","author":"Devroye","year":"2009","journal-title":"ACM Trans. Modlng Comput. Simuln"},{"key":"2023022002192472200_rssb12233-cit-0041","first-page":"33","article-title":"Graph limits and exchangeable random graphs","volume":"28","author":"Diaconis","year":"2008","journal-title":"Rend. Mat. Applic."},{"key":"2023022002192472200_rssb12233-cit-0042","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/0370-2693(87)91197-X","article-title":"Hybrid Monte Carlo","volume":"195","author":"Duane","year":"1987","journal-title":"Phys. Lett."},{"key":"2023022002192472200_rssb12233-cit-0043","volume-title":"Random Graph Dynamics","author":"Durrett","year":"2007"},{"key":"2023022002192472200_rssb12233-cit-0044","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1214\/13-STS422","article-title":"MCMC for normalized random measure mixture models","volume":"28","author":"Favaro","year":"2013","journal-title":"Statist. Sci."},{"key":"2023022002192472200_rssb12233-cit-0045","volume-title":"An Introduction to Probability Theory and Its Applications","author":"Feller","year":"1971"},{"key":"2023022002192472200_rssb12233-cit-0046","doi-asserted-by":"crossref","first-page":"1634","DOI":"10.1214\/aoms\/1177692395","article-title":"A representation of independent increment processes without gaussian components","volume":"43","author":"Ferguson","year":"1972","journal-title":"Ann. Math. Statist."},{"key":"2023022002192472200_rssb12233-cit-0047","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1080\/10618600.2012.738106","article-title":"A brief history of statistical models for network analysis and open challenges","volume":"21","author":"Fienberg","year":"2012","journal-title":"J. Computnl Graph. Statist."},{"key":"2023022002192472200_rssb12233-cit-0048","first-page":"251","article-title":"Funzione caratteristica di un fenomeno aleatorio","volume":"4","author":"de Finetti","year":"1931","journal-title":"Atti R. Acad. Nazn. Linc."},{"key":"2023022002192472200_rssb12233-cit-0049","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1214\/lnms\/1215453566","article-title":"De Finetti's theorem in continuous time","volume":"30","author":"Freedman","year":"1996","journal-title":"Lect. Notes Monogr. Ser."},{"key":"2023022002192472200_rssb12233-cit-0050","volume-title":"Bayesian Data Analysis","author":"Gelman","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-0051","first-page":"273","volume-title":"Proc. 8th Int. Conf. Probability in Banach Spaces","author":"Gin\u00e9","year":"1992"},{"key":"2023022002192472200_rssb12233-cit-0052","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1214\/07-PS092","article-title":"Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws","volume":"4","author":"Gnedin","year":"2007","journal-title":"Probab. Surv."},{"key":"2023022002192472200_rssb12233-cit-0053","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1214\/009117905000000639","article-title":"Asymptotic laws for compositions derived from transformed subordinators","volume":"34","author":"Gnedin","year":"2006","journal-title":"Ann. Probab."},{"key":"2023022002192472200_rssb12233-cit-0054","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1561\/2200000005","article-title":"A survey of statistical network models","volume":"2","author":"Goldenberg","year":"2010","journal-title":"Foundns Trends Mach. Learn."},{"key":"2023022002192472200_rssb12233-cit-0055","first-page":"032819","article-title":"Infinite-degree-corrected stochastic block model","volume":"90","author":"Herlau","year":"2014","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-0056","volume-title":"Advances in Neural Information Processing Systems","author":"Herlau","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-0057","first-page":"3","article-title":"Sampling exponentially tilted stable distributions","volume":"22","author":"Hofert","year":"2011","journal-title":"ACM Trans. Modlng Comput. Simuln"},{"key":"2023022002192472200_rssb12233-cit-0058","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s10588-008-9040-4","article-title":"Multiplicative latent factor models for description and prediction of social networks","volume":"15","author":"Hoff","year":"2009","journal-title":"Computnl Math. Organizn Theory"},{"key":"2023022002192472200_rssb12233-cit-0059","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1198\/016214502388618906","article-title":"Latent space approaches to social network analysis","volume":"97","author":"Hoff","year":"2002","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002192472200_rssb12233-cit-0060","volume-title":"Random Graphs and Complex Networks","author":"van der Hofstad","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-0061","volume-title":"Relations on probability spaces and arrays of random variables","author":"Hoover","year":"1979"},{"key":"2023022002192472200_rssb12233-cit-0062","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1093\/biomet\/73.2.387","article-title":"Survival models for heterogeneous populations derived from stable distributions","volume":"73","author":"Hougaard","year":"1986","journal-title":"Biometrika"},{"key":"2023022002192472200_rssb12233-cit-0063","volume-title":"A unified view of generative models for networks: models, methods, opportunities and challenges","author":"Jacobs","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-0064","volume-title":"Poisson process partition calculus with applications to exchangeable models and bayesian nonparametrics","author":"James","year":"2002"},{"key":"2023022002192472200_rssb12233-cit-0065","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1214\/009053605000000336","article-title":"Bayesian Poisson process partition calculus with an application to Bayesian L\u00e9vy moving averages","volume":"33","author":"James","year":"2005","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-0066","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1111\/j.1467-9469.2008.00609.x","article-title":"Posterior analysis for normalized random measures with independent increments","volume":"36","author":"James","year":"2009","journal-title":"Scand. J. Statist."},{"key":"2023022002192472200_rssb12233-cit-0067","volume-title":"Probability asymptotics: notes on notation","author":"Janson","year":"2011"},{"key":"2023022002192472200_rssb12233-cit-0068","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01063330","article-title":"Exchangeable random measures in the plane","volume":"3","author":"Kallenberg","year":"1990","journal-title":"J. Theoret. Probab."},{"key":"2023022002192472200_rssb12233-cit-0069","volume-title":"Probabilistic Symmetries and Invariance Principles","author":"Kallenberg","year":"2005"},{"key":"2023022002192472200_rssb12233-cit-0070","first-page":"373","article-title":"Central limit theorems for certain infinite urn schemes","volume":"17","author":"Karlin","year":"1967","journal-title":"J. Math. Mech."},{"key":"2023022002192472200_rssb12233-cit-0071","first-page":"016107","article-title":"Stochastic blockmodels and community structure in networks","volume":"83","author":"Karrer","year":"2011","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-0072","first-page":"381","volume-title":"Proc. 21st Natn. Conf. Artificial Intelligence, Boston, July 16th\u201320th","author":"Kemp","year":"2006"},{"key":"2023022002192472200_rssb12233-cit-0073","first-page":"79","article-title":"Zur theorie der unbeschrankt teilbaren Verteilungsgesetze","volume":"2","author":"Khintchine","year":"1937","journal-title":"Mat. Sborn."},{"key":"2023022002192472200_rssb12233-cit-0074","doi-asserted-by":"crossref","first-page":"59","DOI":"10.2140\/pjm.1967.21.59","article-title":"Completely random measures","volume":"21","author":"Kingman","year":"1967","journal-title":"Pacif. J. Math."},{"key":"2023022002192472200_rssb12233-cit-0075","volume-title":"Poisson Processes","author":"Kingman","year":"1993"},{"key":"2023022002192472200_rssb12233-cit-0076","first-page":"83","article-title":"Exchangeable Rasch matrices","volume":"28","author":"Lauritzen","year":"2008","journal-title":"Rend. Mat. Applic. VII"},{"key":"2023022002192472200_rssb12233-cit-0077","doi-asserted-by":"crossref","first-page":"302","DOI":"10.2307\/3214840","article-title":"Stochastic processes directed by randomized time","volume":"30","author":"Lee","year":"1993","journal-title":"J. Appl. Probab."},{"key":"2023022002192472200_rssb12233-cit-0078","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1002\/nav.3800260304","article-title":"Simulation of nonhomogeneous Poisson processes by thinning","volume":"26","author":"Lewis","year":"1979","journal-title":"Navl Res. Logist. Q."},{"key":"2023022002192472200_rssb12233-cit-0079","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1111\/j.1467-9868.2007.00609.x","article-title":"Controlling the reinforcement in Bayesian non-parametric mixture models","volume":"69","author":"Lijoi","year":"2007","journal-title":"J. R. Statist. Soc."},{"key":"2023022002192472200_rssb12233-cit-0080","first-page":"123","volume-title":"Proc. 13th Eur. Young Statisticians Meet.","author":"Lijoi","year":"2003"},{"key":"2023022002192472200_rssb12233-cit-0081","volume-title":"Bayesian Nonparametrics","author":"Lijoi","year":"2010"},{"key":"2023022002192472200_rssb12233-cit-0082","first-page":"1653","article-title":"Investigating nonparametric priors with Gibbs structure","volume":"18","author":"Lijoi","year":"2008","journal-title":"Statist. Sin."},{"key":"2023022002192472200_rssb12233-cit-0083","volume-title":"Advances in Neural Information Processing Systems","author":"Lloyd","year":"2012"},{"key":"2023022002192472200_rssb12233-cit-0084","volume-title":"Large Networks and Graph Limits","author":"Lov\u00e1sz","year":"2013"},{"key":"2023022002192472200_rssb12233-cit-0085","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1016\/j.jctb.2006.05.002","article-title":"Limits of dense graph sequences","volume":"96","author":"Lov\u00e1sz","year":"2006","journal-title":"J. Combin. Theory"},{"key":"2023022002192472200_rssb12233-cit-0086","first-page":"539","volume-title":"Advances in Neural Information Processing Systems","author":"McAuley","year":"2012"},{"key":"2023022002192472200_rssb12233-cit-0087","volume-title":"Advances in Neural Information Processing Systems","author":"Miller","year":"2009"},{"key":"2023022002192472200_rssb12233-cit-0088","volume-title":"Handbook of Markov Chain Monte Carlo","author":"Neal","year":"2011"},{"key":"2023022002192472200_rssb12233-cit-0089","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-27875-4","volume-title":"Sparsity (Graphs, Structures, and Algorithms)","author":"Ne\u0161et\u0159il","year":"2012"},{"key":"2023022002192472200_rssb12233-cit-0090","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1073\/pnas.98.2.404","article-title":"The structure of scientific collaboration networks","volume":"98","author":"Newman","year":"2001","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023022002192472200_rssb12233-cit-0091","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","article-title":"The structure and function of complex networks","volume":"45","author":"Newman","year":"2003","journal-title":"SIAM Rev."},{"key":"2023022002192472200_rssb12233-cit-0092","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780199206650.001.0001","volume-title":"Networks: an Introduction","author":"Newman","year":"2010"},{"key":"2023022002192472200_rssb12233-cit-0093","doi-asserted-by":"crossref","first-page":"26118","DOI":"10.1103\/PhysRevE.64.026118","article-title":"Random graphs with arbitrary degree distributions and their applications","volume":"64","author":"Newman","year":"2001","journal-title":"Phys. Rev. E"},{"key":"2023022002192472200_rssb12233-cit-0094","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1239\/aap\/1143936140","article-title":"On a conditionally Poissonian graph process","volume":"38","author":"Norros","year":"2006","journal-title":"Adv. Appl. Probab."},{"key":"2023022002192472200_rssb12233-cit-0095","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1198\/016214501753208735","article-title":"Estimation and prediction for stochastic blockstructures","volume":"96","author":"Nowicki","year":"2001","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002192472200_rssb12233-cit-0096","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/TIT.1981.1056305","article-title":"On Lewis\u2019 simulation method for point processes","volume":"27","author":"Ogata","year":"1981","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2023022002192472200_rssb12233-cit-0097","volume-title":"Degree-based network models","author":"Olhede","year":"2012"},{"key":"2023022002192472200_rssb12233-cit-0098","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.socnet.2009.02.002","article-title":"Clustering in weighted networks","volume":"31","author":"Opsahl","year":"2009","journal-title":"Socl Netwrks"},{"key":"2023022002192472200_rssb12233-cit-0099","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1109\/TPAMI.2014.2334607","article-title":"Bayesian models of graphs, arrays and other exchangeable random structures","volume":"37","author":"Orbanz","year":"2015","journal-title":"IEEE Trans. Pattn Anal. Mach. Intell."},{"key":"2023022002192472200_rssb12233-cit-0100","volume-title":"Proc. 29th Int. Conf. Machine Learning, Edinburgh","author":"Palla","year":"2012"},{"key":"2023022002192472200_rssb12233-cit-0101","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198506263.001.0001","volume-title":"Random Geometric Graphs","author":"Penrose","year":"2003"},{"key":"2023022002192472200_rssb12233-cit-0102","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF01213386","article-title":"Exchangeable and partially exchangeable random partitions","volume":"102","author":"Pitman","year":"1995","journal-title":"Probab. Theory Reltd Flds"},{"key":"2023022002192472200_rssb12233-cit-0103","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1214\/lnms\/1215453576","article-title":"Some developments of the Blackwell-MacQueen urn scheme","author":"Pitman","year":"1996","journal-title":"Statistics, Probability and Game Theory: Papers in Honor of David Blackwell"},{"key":"2023022002192472200_rssb12233-cit-0104","first-page":"1","article-title":"Poisson-Kingman partitions","volume":"40","author":"Pitman","year":"2003","journal-title":"Lect. Notes Monogr. Ser."},{"key":"2023022002192472200_rssb12233-cit-0105","volume-title":"\u00c9cole d\u2019Et\u00e9 de Probabilit\u00e9s de Saint-Flour XXXII\u20132002","author":"Pitman","year":"2006"},{"key":"2023022002192472200_rssb12233-cit-0106","volume-title":"Random probability measures derived from increasing additive processes and their application to Bayesian statistics","author":"Pr\u00fcnster","year":"2002"},{"key":"2023022002192472200_rssb12233-cit-0107","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1214\/aos\/1051027881","article-title":"Distributional results for means of normalized random measures with independent increments","volume":"31","author":"Regazzini","year":"2003","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-0108","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75953-1","volume-title":"Extreme Values, Point Processes and Regular Variation","author":"Resnick","year":"1987"},{"key":"2023022002192472200_rssb12233-cit-0109","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1214\/11-AOS887","article-title":"Spectral clustering and the high-dimensional stochastic blockmodel","volume":"39","author":"Rohe","year":"2011","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-0110","volume-title":"Exchangeable random measures for sparse and modular graphs with overlapping communities","author":"Todeschini","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-0111","volume-title":"The class of random graphs arising from exchangeable random measures","author":"Veitch","year":"2015"},{"key":"2023022002192472200_rssb12233-cit-0112","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":"2023022002192472200_rssb12233-cit-0113","volume-title":"Nonparametric graphon estimation. Preprint arXiv:1309.5936","author":"Wolfe","year":"2013"},{"key":"2023022002192472200_rssb12233-cit-0114","doi-asserted-by":"crossref","first-page":"2266","DOI":"10.1214\/12-AOS1036","article-title":"Consistency of community detection in networks under degree-corrected stochastic block models","volume":"40","author":"Zhao","year":"2012","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-1001","first-page":"1981","article-title":"Mixed membership stochastic blockmodels","volume":"9","author":"Airoldi","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"2023022002192472200_rssb12233-cit-1002","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1038\/43601","article-title":"Internet: diameter of the World-Wide Web","volume":"401","author":"Albert","year":"1999","journal-title":"Nature"},{"key":"2023022002192472200_rssb12233-cit-1003","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1214\/aop\/1176989404","article-title":"The continuum random tree III","volume":"21","author":"Aldous","year":"1993","journal-title":"Ann. Probab."},{"key":"2023022002192472200_rssb12233-cit-1004","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/0047-259X(81)90099-3","article-title":"Representations for partially exchangeable arrays of random variables","volume":"11","author":"Aldous","year":"1981","journal-title":"J. Multiv. Anal."},{"key":"2023022002192472200_rssb12233-cit-1005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/EJP.v19-2920","article-title":"Scale-invariant random spatial networks","volume":"19","author":"Aldous","year":"2014","journal-title":"Electron. J. Probab."},{"key":"2023022002192472200_rssb12233-cit-1006","doi-asserted-by":"crossref","first-page":"8782","DOI":"10.1073\/pnas.1304329110","article-title":"True scale-invariant random spatial networks","volume":"110","author":"Aldous","year":"2013","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023022002192472200_rssb12233-cit-1007","first-page":"1","article-title":"The objective method: probabilistic combinatorial optimization and local weak convergence","volume":"110","author":"Aldous","year":"2004","journal-title":"Encycl. Math. Sci."},{"key":"2023022002192472200_rssb12233-cit-1008","first-page":"045102","article-title":"Entropy measures for networks: toward an information theory of complex topologies","volume":"80","author":"Anand","year":"2009","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-1009","first-page":"011116","article-title":"Gibbs entropy of network ensembles by cavity methods","volume":"82","author":"Anand","year":"2010","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-1010","volume-title":"Asymptotic analysis of normalized random measures with independent increments","author":"Arbel","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1011","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1007\/s11222-015-9549-6","article-title":"A blocked Gibbs sampler for NGG-mixture models via a priori truncation","volume":"26","author":"Argiento","year":"2016","journal-title":"Statist. Comput."},{"key":"2023022002192472200_rssb12233-cit-1012","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s13171-015-0071-x","article-title":"A limit theorem for scaled eigenvectors of random dot product graphs","volume":"78","author":"Athreya","year":"2016","journal-title":"Sankhya"},{"key":"2023022002192472200_rssb12233-cit-1013","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1007\/s11222-015-9562-9","article-title":"de Finetti priors using Markov Chain Monte Carlo computations","volume":"25","author":"Bacallado","year":"2015","journal-title":"Statist. Comput."},{"key":"2023022002192472200_rssb12233-cit-1014","volume-title":"Network Science","author":"Barab\u00e1si","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1015","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Barab\u00e1si","year":"1999","journal-title":"Science"},{"key":"2023022002192472200_rssb12233-cit-1016","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1126\/science.1137521","article-title":"Fast routing in road networks with transit nodes","volume":"316","author":"Bast","year":"2007","journal-title":"Science"},{"key":"2023022002192472200_rssb12233-cit-1017","doi-asserted-by":"crossref","DOI":"10.1080\/01621459.2016.1240081","article-title":"Statistical tests for large tree-structured data","author":"Bharath","year":"2017","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002192472200_rssb12233-cit-1018","doi-asserted-by":"crossref","first-page":"21068","DOI":"10.1073\/pnas.0907096106","article-title":"A nonparametric view of network models and Newman\u2013Girvan and other modularities","volume":"106","author":"Bickel","year":"2009","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023022002192472200_rssb12233-cit-1019","first-page":"121","article-title":"Variational inference for Dirichlet process mixtures","volume":"1","author":"Blei","year":"2006","journal-title":"Baysn Anal."},{"key":"2023022002192472200_rssb12233-cit-1020","volume-title":"Hierarchical q-latent feature models","author":"Bloem-Reddy","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1021","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.csda.2004.02.004","article-title":"Statistical analysis of financial networks","volume":"48","author":"Boginski","year":"2005","journal-title":"Computnl Statist. Data Anal."},{"key":"2023022002192472200_rssb12233-cit-1022","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/rsa.20168","article-title":"The phase transition in inhomogeneous random graphs","volume":"31","author":"Bollob\u00e1s","year":"2007","journal-title":"Rand. Struct. Algs"},{"key":"2023022002192472200_rssb12233-cit-1023","first-page":"211","volume-title":"Surveys in Combinatorics","author":"Bollob\u00e1s","year":"2009"},{"key":"2023022002192472200_rssb12233-cit-1024","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1126\/science.1175509","article-title":"GABAergic hub neurons orchestrate synchrony in developing hippocampal networks","volume":"326","author":"Bonifazi","year":"2009","journal-title":"Science"},{"key":"2023022002192472200_rssb12233-cit-1025","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.socnet.2005.11.005","article-title":"A graph-theoretic perspective on centrality","volume":"28","author":"Borgatti","year":"2006","journal-title":"Socl Netwrks"},{"key":"2023022002192472200_rssb12233-cit-1026","volume-title":"Sparse exchangeable graphs and their limits via graphon processes","author":"Borgs","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1027","volume-title":"An Lp theory of sparse graph convergence: I, Limits, sparse random graph models, and power law distributions","author":"Borgs","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-1028","article-title":"Private graphon estimation for sparse graphs","author":"Borgs","year":"2015","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2023022002192472200_rssb12233-cit-1029","article-title":"The bouncy particle sampler: a non-reversible rejection-free Markov chain Monte Carlo method","author":"Bouchard-C\u00f4te","year":"2017","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002192472200_rssb12233-cit-1030","first-page":"107","article-title":"The anatomy of a large-scale hypertextual Web search engine","volume":"30","author":"Brin","year":"1998","journal-title":"Comput. Netwrks"},{"key":"2023022002192472200_rssb12233-cit-1031","volume-title":"Proc. Wrkshp Bayesian Nonparametrics: the Next Generation","author":"Broderick","year":"2015"},{"key":"2023022002192472200_rssb12233-cit-1032","first-page":"4249","volume-title":"Advances in Neural Information Processing Systems","author":"Cai","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1033","volume-title":"Hierarchical and nested random probability measures with statistical applications","author":"Camerlenghi","year":"2015"},{"key":"2023022002192472200_rssb12233-cit-1034","volume-title":"Exchangeable trait allocations","author":"Campbell","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1035","volume-title":"Truncated random measures","author":"Campbell","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1036","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1080\/10618600.2012.638220","article-title":"Efficient Bayesian inference for generalized Bradley-Terry models","volume":"21","author":"Caron","year":"2012","journal-title":"J. Computnl Graph. Statist."},{"key":"2023022002192472200_rssb12233-cit-1037","volume-title":"On sparsity and power-law properties of graphs based on exchangeable point processes","author":"Caron","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1038","first-page":"1145","article-title":"Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes","volume":"82","author":"Caron","year":"2014","journal-title":"Ann. Appl. Statist."},{"key":"2023022002192472200_rssb12233-cit-1039","volume-title":"Private graphon estimation for sparse graphs","author":"Chayes","year":"2015"},{"key":"2023022002192472200_rssb12233-cit-1040","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1137\/070710111","article-title":"Power-law distributions in empirical data","volume":"51","author":"Clauset","year":"2009","journal-title":"SIAM Rev."},{"key":"2023022002192472200_rssb12233-cit-1041","volume-title":"A framework for statistical network modeling","author":"Crane","year":"2015"},{"key":"2023022002192472200_rssb12233-cit-1042","volume-title":"Edge exchangeable models for network data","author":"Crane","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1043","first-page":"1695","article-title":"The igraph software package for complex network research","volume":"18","author":"Cs\u00e1rdi","year":"2006","journal-title":"InterJ. Complx Syst."},{"key":"2023022002192472200_rssb12233-cit-1044","doi-asserted-by":"crossref","first-page":"178701","DOI":"10.1103\/PhysRevLett.107.178701","article-title":"All scale-free networks are sparse","volume":"107","author":"Del Genio","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"2023022002192472200_rssb12233-cit-1045","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1080\/00018730110112519","article-title":"Evolution of networks","volume":"51","author":"Dorogovtsev","year":"2002","journal-title":"Adv. Phys."},{"key":"2023022002192472200_rssb12233-cit-1046","volume-title":"Artificial Intelligence and Statistics","author":"Doshi-Velez","year":"2009"},{"key":"2023022002192472200_rssb12233-cit-1047","article-title":"Nonparametric Bayes modeling of populations of networks","author":"Durante","year":"2017","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002192472200_rssb12233-cit-1048","first-page":"265","article-title":"Calibrating noise to sensitivity in private data analysis","author":"Dwork","year":"2006","journal-title":"Theory of Cryptography"},{"key":"2023022002192472200_rssb12233-cit-1049","doi-asserted-by":"crossref","DOI":"10.1016\/j.spasta.2017.04.007","article-title":"Analysing highly complex and highly structured point patterns in space","author":"Eckardt","year":"2017","journal-title":"Spatl Statist."},{"key":"2023022002192472200_rssb12233-cit-1050","article-title":"Point patterns occurring on complex structures in space and space-time: an alternative network approach","author":"Eckardt","year":"2017","journal-title":"J. Computnl Graph. Statist."},{"key":"2023022002192472200_rssb12233-cit-1051","article-title":"Analysing multivariate spatial point processes with continuous marks: a graphical modelling approach","author":"Eckardt","year":"2017","journal-title":"Int. Statist. Rev."},{"key":"2023022002192472200_rssb12233-cit-1052","first-page":"066102","article-title":"Quantifying network heterogeneity","volume":"82","author":"Estrada","year":"2010","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-1053","first-page":"036111","article-title":"Communicability in complex networks","volume":"77","author":"Estrada","year":"2008","journal-title":"Phys. Rev"},{"key":"2023022002192472200_rssb12233-cit-1054","first-page":"500","article-title":"Communicability graph and community structures in complex networks","volume":"214","author":"Estrada","year":"2009","journal-title":"Appl. Math. Computn"},{"key":"2023022002192472200_rssb12233-cit-1055","volume-title":"Testing network structure using relations between small subgraph probabilities","author":"Gao","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1056","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1561\/2200000005","article-title":"A survey of statistical network models","volume":"2","author":"Goldenberg","year":"2010","journal-title":"Foundns Trends Mach. Learn."},{"key":"2023022002192472200_rssb12233-cit-1057","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1111\/j.1467-985X.2006.00412.x","article-title":"Analysis of Irish third-level college applications data","volume":"169","author":"Gormley","year":"2006","journal-title":"J. R. Statist. Soc."},{"key":"2023022002192472200_rssb12233-cit-1058","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1111\/j.1467-9892.2004.01866.x","article-title":"A dependence metric for possibly nonlinear processes","volume":"25","author":"Granger","year":"2004","journal-title":"J. Time Ser. Anal."},{"key":"2023022002192472200_rssb12233-cit-1059","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1111\/rssb.12002","article-title":"Comparing distributions by using dependent normalized random-measure mixtures","volume":"75","author":"Griffin","year":"2013","journal-title":"J. R. Statist. Soc."},{"key":"2023022002192472200_rssb12233-cit-1060","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1111\/rssb.12176","article-title":"Compound random measures and their use in Bayesian nonparametrics","volume":"79","author":"Griffin","year":"2017","journal-title":"J. R. Statist. Soc."},{"key":"2023022002192472200_rssb12233-cit-1061","first-page":"4260","volume-title":"Advances in Neural Information Processing Systems","author":"Herlau","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1062","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1198\/016214502388618906","article-title":"Latent space approaches to social network analysis","volume":"97","author":"Hoff","year":"2002","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002192472200_rssb12233-cit-1063","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0378-8733(83)90021-7","article-title":"Stochastic blockmodels: first steps","volume":"5","author":"Holland","year":"1983","journal-title":"Socl Netwrks"},{"key":"2023022002192472200_rssb12233-cit-1064","volume-title":"Relations on probability spaces and arrays of random variables","author":"Hoover","year":"1979"},{"key":"2023022002192472200_rssb12233-cit-1065","volume-title":"Poisson process partition calculus with applications to exchangeable models and Bayesian nonparametrics","author":"James","year":"2002"},{"key":"2023022002192472200_rssb12233-cit-1066","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1111\/j.1467-9469.2008.00609.x","article-title":"Posterior analysis for normalized random measures with independent increments","volume":"36","author":"James","year":"2009","journal-title":"Scand. J. Statist."},{"key":"2023022002192472200_rssb12233-cit-1067","volume-title":"Graphons and cut metric on \u03c3-finite measure spaces","author":"Janson","year":"2010"},{"key":"2023022002192472200_rssb12233-cit-1068","volume-title":"On edge exchangeable random graphs","author":"Janson","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1069","volume-title":"On convergence for graphexes","author":"Janson","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1070","doi-asserted-by":"crossref","first-page":"2694","DOI":"10.1214\/15-AOP1032","article-title":"Improper Poisson line process as SIRSN in any dimension","volume":"44","author":"Kahn","year":"2016","journal-title":"Ann. Probab."},{"key":"2023022002192472200_rssb12233-cit-1071","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01063330","article-title":"Exchangeable random measures in the plane","volume":"3","author":"Kallenberg","year":"1990","journal-title":"J. Theoret. Probab."},{"key":"2023022002192472200_rssb12233-cit-1072","volume-title":"Probabilistic Symmetries and Invariance Principles","author":"Kallenberg","year":"2005"},{"key":"2023022002192472200_rssb12233-cit-1073","first-page":"016107","article-title":"Stochastic blockmodels and community structure in networks","volume":"83","author":"Karrer","year":"2011","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-1074","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1214\/14-AOP935","article-title":"From random lines to metric spaces","volume":"45","author":"Kendall","year":"2017","journal-title":"Ann. Probab."},{"key":"2023022002192472200_rssb12233-cit-1075","doi-asserted-by":"crossref","first-page":"188701","DOI":"10.1103\/PhysRevLett.106.188701","article-title":"Extreme events on complex networks","volume":"106","author":"Kishore","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"2023022002192472200_rssb12233-cit-1076","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-88146-1","volume-title":"Statistical Analysis of Network Data","author":"Kolaczyk","year":"2009"},{"key":"2023022002192472200_rssb12233-cit-1077","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4939-0983-4","volume-title":"Statistical Analysis of Network Data with R","author":"Kolaczyk","year":"2014"},{"key":"2023022002192472200_rssb12233-cit-1078","doi-asserted-by":"crossref","first-page":"2148","DOI":"10.1214\/aos\/1069362315","article-title":"Markov properties of nonrecursive causal models","volume":"24","author":"Koster","year":"1996","journal-title":"Ann. Statist."},{"key":"2023022002192472200_rssb12233-cit-1079","doi-asserted-by":"crossref","first-page":"218301","DOI":"10.1103\/PhysRevLett.117.218301","article-title":"Structural transitions in densifying networks","volume":"117","author":"Lambiotte","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"2023022002192472200_rssb12233-cit-1080","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1016\/j.disc.2007.07.104","article-title":"Pebble game algorithms and sparse graphs","volume":"308","author":"Lee","year":"2008","journal-title":"Discr. Math."},{"key":"2023022002192472200_rssb12233-cit-1081","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.jmva.2010.10.008","article-title":"Vectors of Poisson-Dirichlet processes","volume":"102","author":"Leisen","year":"2011","journal-title":"J. Multiv. Anal."},{"key":"2023022002192472200_rssb12233-cit-1082","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1111\/j.1467-9868.2007.00609.x","article-title":"Controlling the reinforcement in Bayesian non-parametric mixture models","volume":"69","author":"Lijoi","year":"2007","journal-title":"J. R. Statist. Soc."},{"key":"2023022002192472200_rssb12233-cit-1083","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1089\/cmb.2008.0043","article-title":"A Bayesian nonparametric approach for comparing clustering structures in EST libraries","volume":"15","author":"Lijoi","year":"2008","journal-title":"J. Computnl Biol."},{"key":"2023022002192472200_rssb12233-cit-10150","doi-asserted-by":"crossref","DOI":"10.1002\/047172209X","volume-title":"Random Graphs for Statistical Pattern Recognition","author":"Marchette","year":"2004"},{"key":"2023022002192472200_rssb12233-cit-1084","doi-asserted-by":"crossref","first-page":"283","DOI":"10.2307\/3315511","article-title":"Approximating distributions of random functionals of Ferguson\u2013Dirichlet priors","volume":"26","author":"Muliere","year":"1998","journal-title":"Can. J. Statist."},{"key":"2023022002192472200_rssb12233-cit-1085","first-page":"173","volume-title":"Proc. Symp. Security and Privacy","author":"Narayanon","year":"2009"},{"key":"2023022002192472200_rssb12233-cit-1086","first-page":"1","volume-title":"Handbook of Markov Chain Monte Carlo","author":"Neal","year":"2011"},{"key":"2023022002192472200_rssb12233-cit-1087","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780199206650.001.0001","volume-title":"Networks: an Introduction","author":"Newman","year":"2010"},{"key":"2023022002192472200_rssb12233-cit-1088","volume-title":"Reciprocal graphical models for integrative gene regulatory network analysis","author":"Ni","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1089","volume-title":"Random dot product graphs: a model for social networks","author":"Nickel","year":"2006"},{"key":"2023022002192472200_rssb12233-cit-1090","volume-title":"Subsampling and invariance in networks","author":"Orbanz","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1091","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1109\/TPAMI.2014.2334607","article-title":"Bayesian models of graphs, arrays and other exchangeable random structures","volume":"37","author":"Orbanz","year":"2015","journal-title":"IEEE Trans. Pattn Anal. Mach. Intell."},{"key":"2023022002192472200_rssb12233-cit-1092","volume-title":"A Bayesian nonparametric model for sparse dynamic networks","author":"Palla","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1093","first-page":"066117","article-title":"Statistical mechanics of networks","volume":"70","author":"Park","year":"2004","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-1094","first-page":"1","volume-title":"Statistics and Science: a Festschrift for Terry Speed","author":"Pitman","year":"2003"},{"key":"2023022002192472200_rssb12233-cit-1095","volume-title":"R: a Language and Environment for Statistical Computing","author":"R Core Team","year":"2017"},{"key":"2023022002192472200_rssb12233-cit-1096","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1198\/016214508000000553","article-title":"The nested Dirichlet process","volume":"103","author":"Rodr\u00edguez","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002192472200_rssb12233-cit-1097","first-page":"046113","article-title":"Scale-free networks with an exponent less than two","volume":"73","author":"Seyed-Allaei","year":"2006","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-1098","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/13-SS103","article-title":"Analyzing complex functional brain networks: fusing statistics and network science to understand the brain","volume":"7","author":"Simpson","year":"2013","journal-title":"Statist. Surv."},{"key":"2023022002192472200_rssb12233-cit-1099","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1186\/1471-2105-13-328","article-title":"Comparison of co-expression measures: mutual information, correlation, and model based indices","volume":"13","author":"Song","year":"2012","journal-title":"BMC Bioinform."},{"key":"2023022002192472200_rssb12233-cit-1100","volume-title":"Stan Modeling Language Users Guide and Reference Manual, Version 2.15.0","author":"Stan Development Team","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1101","first-page":"022302","article-title":"Scale-free networks with exponent one","volume":"94","author":"Tim\u00e1r","year":"2016","journal-title":"Phys. Rev."},{"key":"2023022002192472200_rssb12233-cit-1102","volume-title":"Exchangeable random measures for sparse and modular graphs with overlapping communities","author":"Todeschini","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1103","first-page":"1307","volume-title":"Proc. 22nd Int. Conf. World Wide Web","author":"Ugander","year":"2013"},{"key":"2023022002192472200_rssb12233-cit-1104","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/rssa.12124","article-title":"Statistical modelling of citation exchange between statistics journals (with discussion)","volume":"179","author":"Varin","year":"2016","journal-title":"J. R. Statist. Soc."},{"key":"2023022002192472200_rssb12233-cit-1105","volume-title":"The class of random graphs arising from exchangeable random measures","author":"Veitch","year":"2015"},{"key":"2023022002192472200_rssb12233-cit-1106","volume-title":"Sampling and estimation for (sparse) exchangeable graphs","author":"Veitch","year":"2016"},{"key":"2023022002192472200_rssb12233-cit-1107","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","article-title":"A tutorial on spectral clustering","volume":"17","author":"Von Luxburg","year":"2007","journal-title":"Statist. Comput."},{"key":"2023022002192472200_rssb12233-cit-1108","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of small-world networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"2023022002192472200_rssb12233-cit-1109","first-page":"3","article-title":"A geometric view on Pearson's correlation coefficient and a generalization of it to non-linear dependencies","volume":"30","author":"Wijayatunga","year":"2016","journal-title":"Rat. Math."},{"key":"2023022002192472200_rssb12233-cit-1110","first-page":"1","article-title":"Nonparametric network models for link prediction","volume":"17","author":"Williamson","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"2023022002192472200_rssb12233-cit-1111","volume-title":"Nonparametric graphon estimation","author":"Wolfe","year":"2013"},{"key":"2023022002192472200_rssb12233-cit-1112","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1007\/978-3-540-77004-6_11","volume-title":"Proc. Int. Wrkshp Algorithms and Models for the Web-graph","author":"Young","year":"2007"},{"key":"2023022002192472200_rssb12233-cit-1113","first-page":"1135","article-title":"Infinite edge partition models for overlapping community detection and link prediction","volume":"38","author":"Zhou","year":"2015","journal-title":"Proc. Mach. Learn. Res."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12233","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12233","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12233","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/api.wiley.com\/onlinelibrary\/chorus\/v1\/articles\/10.1111%2Frssb.12233","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/79\/5\/1295\/49269335\/jrsssb_79_5_1295.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/79\/5\/1295\/49269335\/jrsssb_79_5_1295.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T01:53:00Z","timestamp":1719453180000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/79\/5\/1295\/7041107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,23]]},"references-count":228,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2017,9,23]]},"published-print":{"date-parts":[[2017,11,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12233","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2017,11]]},"published":{"date-parts":[[2017,9,23]]}}}