{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:34:45Z","timestamp":1762868085499,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,3,11]],"date-time":"2020-03-11T00:00:00Z","timestamp":1583884800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,3,11]],"date-time":"2020-03-11T00:00:00Z","timestamp":1583884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004744","name":"Innoviris","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004744","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EPJ Data Sci."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Many times the nodes of a complex network, whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy reasons. A\u00a0common example is the geographic position: one may uncover communities in a network of places, or of individuals identified with their typical geographical position, and then aggregate these places into larger entities, such as municipalities, thus obtaining another network. The communities found in the networks obtained at various levels of aggregation may exhibit various degrees of similarity, from full alignment to perfect independence. This is akin to the problem of ecological and atomic fallacies in statistics, or to the Modified Areal Unit Problem in geography.<\/jats:p><jats:p>We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure. We illustrate its relevance on real-world examples (mobile phone and Twitter reply-to networks). Our main message is that any node-partitioning analysis performed on aggregated networks should be interpreted with caution, as the outcome may be strongly influenced by the level of the aggregation.<\/jats:p>","DOI":"10.1140\/epjds\/s13688-020-00223-0","type":"journal-article","created":{"date-parts":[[2020,3,11]],"date-time":"2020-03-11T08:02:42Z","timestamp":1583913762000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Measuring the effect of node aggregation on community detection"],"prefix":"10.1140","volume":"9","author":[{"given":"Y\u00e9rali","family":"Gandica","sequence":"first","affiliation":[]},{"given":"Adeline","family":"Decuyper","sequence":"additional","affiliation":[]},{"given":"Christophe","family":"Cloquet","sequence":"additional","affiliation":[]},{"given":"Isabelle","family":"Thomas","sequence":"additional","affiliation":[]},{"given":"Jean-Charles","family":"Delvenne","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,3,11]]},"reference":[{"issue":"3\u20135","key":"223_CR1","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.physrep.2009.11.002","volume":"486","author":"S Fortunato","year":"2010","unstructured":"Fortunato S (2010) Community detection in graphs. Phys Rep 486(3\u20135):75\u2013174. https:\/\/doi.org\/10.1016\/j.physrep.2009.11.002","journal-title":"Phys Rep"},{"issue":"2","key":"223_CR2","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1111\/j.2517-6161.1951.tb00088.x","volume":"13","author":"E. H. Simpson","year":"1951","unstructured":"Simpson EH (1951) The interpretation of interaction in contingency tables. J\u00a0R Stat Soc, Ser\u00a0B, Methodol","journal-title":"Journal of the Royal Statistical Society: Series B (Methodological)"},{"issue":"338","key":"223_CR3","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1080\/01621459.1972.10482387","volume":"67","author":"CR Blyth","year":"1972","unstructured":"Blyth CR (1972) On Simpson\u2019s paradox and the sure-thing principle. J\u00a0Am Stat Assoc 67(338):364\u2013366","journal-title":"J\u00a0Am Stat Assoc"},{"issue":"3","key":"223_CR4","doi-asserted-by":"publisher","first-page":"351","DOI":"10.2307\/2087176","volume":"15","author":"WS Robinson","year":"1950","unstructured":"Robinson WS (1950) Ecological correlations and the behavior of individuals. Am Sociol Rev 15(3):351\u2013357","journal-title":"Am Sociol Rev"},{"key":"223_CR5","doi-asserted-by":"crossref","unstructured":"Gehlke CE, Biehl K (1934) Certain effects of grouping upon the size of the correlation coefficient in census tract material. J\u00a0Am Stat Assoc","DOI":"10.2307\/2277827"},{"key":"223_CR6","volume-title":"The modifiable areal unit problem","author":"S Openshaw","year":"1984","unstructured":"Openshaw S (1984) The modifiable areal unit problem. Geo Abstracts University of East Anglia"},{"key":"223_CR7","volume-title":"The sage handbook of spatial analysis","author":"D Wong","year":"2009","unstructured":"Wong D (2009) The modifiable areal unit problem (MAUP). In: Fotheringham AS, Rogerson PA (eds) The sage handbook of spatial analysis. Sage, Los Angeles"},{"key":"223_CR8","unstructured":"Cucuringu M, Rombach MP, Lee SH, Porter MA (2014) Detection of core-periphery structure in networks using spectral methods and geodesic paths. arXiv preprint arXiv:1410.6572"},{"key":"223_CR9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.088701","volume":"115","author":"M Newman","year":"2015","unstructured":"Newman M, Peixoto TP (2015) Generalized communities in networks. Phys Rev Lett 115:8","journal-title":"Phys Rev Lett"},{"issue":"2","key":"223_CR10","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1561\/2200000005","volume":"2","author":"A Goldenberg","year":"2010","unstructured":"Goldenberg A, Zheng AX, Fienberg SE, Airoldi EM (2010) A\u00a0survey of statistical network models. Found Trends Mach Learn 2(2):129\u2013233","journal-title":"Found Trends Mach Learn"},{"issue":"1","key":"223_CR11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.016110","volume":"74","author":"J Reichardt","year":"2006","unstructured":"Reichardt J, Bornholdt S (2006) Statistical mechanics of community detection. Phys Rev\u00a0E 74(1):016110. https:\/\/doi.org\/10.1103\/PhysRevE.74.016110","journal-title":"Phys Rev\u00a0E"},{"key":"223_CR12","volume-title":"Dynamics on and of complex networks","author":"JC Delvenne","year":"2013","unstructured":"Delvenne JC, Schaub MT, Yaliraki SN, Barahona M (2013) The stability of a graph partition: a dynamics-based framework for community detection. In: Dynamics on and of complex networks. Springer, New York"},{"key":"223_CR13","unstructured":"Peel L, Larremore DB, Clauset A (2016) The ground truth about metadata and community detection in networks. arXiv preprint arXiv:1608.05878"},{"key":"223_CR14","unstructured":"Schaub M, Delvenne JC, Rosvall M, Lambiotte R (2016) The many facets of community detection in complex networks. arXiv preprint arXiv:1611.07769"},{"issue":"4","key":"223_CR15","doi-asserted-by":"publisher","DOI":"10.1145\/3091106","volume":"50","author":"T Chakraborty","year":"2017","unstructured":"Chakraborty T, Dalmia A, Mukherjee A, Ganguly N (2017) Metrics for community analysis: a survey. ACM Comput Surv 50(4):54. https:\/\/doi.org\/10.1145\/3091106","journal-title":"ACM Comput Surv"},{"issue":"2","key":"223_CR16","volume":"69","author":"MEJ Newman","year":"2004","unstructured":"Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev\u00a0E 69(2):026113","journal-title":"Phys Rev\u00a0E"},{"key":"223_CR17","volume":"76","author":"J Reichardt","year":"2007","unstructured":"Reichardt J, Bornholdt S (2007) Partitioning and modularity of graphs with arbitrary degree distribution. Phys Rev\u00a0E 76:015102","journal-title":"Phys Rev\u00a0E"},{"issue":"4","key":"223_CR18","doi-asserted-by":"publisher","first-page":"1118","DOI":"10.1073\/pnas.0706851105","volume":"105","author":"M Rosvall","year":"2008","unstructured":"Rosvall M, Bergstrom CT (2008) Maps of random walks on complex networks reveal community structure. Proc Natl Acad Sci 105(4):1118\u20131123. https:\/\/doi.org\/10.1073\/pnas.0706851105","journal-title":"Proc Natl Acad Sci"},{"key":"223_CR19","volume-title":"Proceedings of the symposium on foundations of computer science","author":"R Kannan","year":"2000","unstructured":"Kannan R, Vempala S, Vetta A (2000) On clusterings: good, bad and spectral. In: Proceedings of the symposium on foundations of computer science"},{"issue":"8","key":"223_CR20","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1109\/34.868688","volume":"22","author":"S Jianbo","year":"2000","unstructured":"Jianbo S, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888\u2013905. https:\/\/doi.org\/10.1109\/34.868688","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"223_CR21","unstructured":"van Dongen S (2000) A\u00a0cluster algorithm for graphs. RFC INS-R001, CWI, The Netherlands"},{"issue":"2","key":"223_CR22","doi-asserted-by":"publisher","first-page":"191","DOI":"10.7155\/jgaa.00124","volume":"10","author":"M Latapy","year":"2006","unstructured":"Latapy M, Pons P (2006) Computing communities in large networks using random walks. J\u00a0Graph Algorithms Appl 10(2):191\u2013218","journal-title":"J\u00a0Graph Algorithms Appl"},{"key":"223_CR23","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1140\/epjb\/e2004-00124-y","volume":"38","author":"MEJ Newman","year":"2004","unstructured":"Newman MEJ (2004) Detecting community structure in networks. Eur Phys J\u00a0B 38:321\u2013330","journal-title":"Eur Phys J\u00a0B"},{"issue":"10","key":"223_CR24","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2008\/10\/P10008","volume":"2008","author":"VD Blondel","year":"2008","unstructured":"Blondel VD, Guillaume J-L, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J\u00a0Stat Mech Theory Exp 2008(10):P10008","journal-title":"J\u00a0Stat Mech Theory Exp"},{"issue":"2","key":"223_CR25","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1109\/TNSE.2015.2391998","volume":"1","author":"R Lambiotte","year":"2014","unstructured":"Lambiotte R, Delvenne JC, Barahona M (2014) Random walks, Markov processes and the multiscale modular organization of complex networks. IEEE Trans Netw Sci Eng 1(2):76\u201390","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"223_CR26","first-page":"2","volume-title":"Computer vision and pattern recognition proceedings 2003 IEEE computer society conference on","author":"L Ana","year":"2003","unstructured":"Ana L, Jain AK (2003) Robust data clustering. In: Computer vision and pattern recognition proceedings 2003 IEEE computer society conference on, vol\u00a02, pp\u00a02\u2013128"},{"key":"223_CR27","doi-asserted-by":"crossref","unstructured":"Thomas I, Adam A, Verhetsel A (2017) Migration and commuting interactions fields: a\u00a0new geography with community detection algorithm? Belgeo 2017(4)","DOI":"10.4000\/belgeo.20507"},{"key":"223_CR28","volume-title":"Proceedings of the 25th international conference on world wide web","author":"D Hristova","year":"2016","unstructured":"Hristova D, Williams MJ, Musolesi M, Panzarasa P, Mascolo C (2016) Measuring urban social DiversityUsing interconnected geo-social networks. In: Proceedings of the 25th international conference on world wide web"},{"issue":"2","key":"223_CR29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.028701","volume":"94","author":"M Rosvall","year":"2005","unstructured":"Rosvall M, Trusina A, Minnhagen P, Sneppen K (2005) Networks and cities: an information perspective. Phys Rev Lett 94(2):028701","journal-title":"Phys Rev Lett"},{"issue":"4","key":"223_CR30","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s10109-018-0279-0","volume":"20","author":"A Adam","year":"2018","unstructured":"Adam A, Delvenne JC, Thomas I (2018) Detecting communities with the multi-scale Louvain method: robustness test on the metropolitan area of Brussels. J\u00a0Geogr Syst 20(4):363\u2013386","journal-title":"J\u00a0Geogr Syst"}],"container-title":["EPJ Data Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1140\/epjds\/s13688-020-00223-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1140\/epjds\/s13688-020-00223-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1140\/epjds\/s13688-020-00223-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T23:35:55Z","timestamp":1722555355000},"score":1,"resource":{"primary":{"URL":"https:\/\/epjdatascience.springeropen.com\/articles\/10.1140\/epjds\/s13688-020-00223-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,11]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["223"],"URL":"https:\/\/doi.org\/10.1140\/epjds\/s13688-020-00223-0","relation":{},"ISSN":["2193-1127"],"issn-type":[{"type":"electronic","value":"2193-1127"}],"subject":[],"published":{"date-parts":[[2020,3,11]]},"assertion":[{"value":"3 June 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"6"}}