{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:24:59Z","timestamp":1772295899051,"version":"3.50.1"},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,4,1]]},"DOI":"10.1093\/comnet\/cnx028","type":"journal-article","created":{"date-parts":[[2017,7,3]],"date-time":"2017-07-03T19:14:36Z","timestamp":1499109276000},"page":"157-172","source":"Crossref","is-referenced-by-count":11,"title":["Geometric multiscale community detection: Markov stability and vector partitioning"],"prefix":"10.1093","volume":"6","author":[{"given":"Zijing","family":"Liu","sequence":"first","affiliation":[{"name":"Departments of Mathematics and Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mauricio","family":"Barahona","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2017,7,26]]},"reference":[{"key":"key\n\t\t\t\t20180321100315_B1","first-page":"221","article-title":"The stability of a graph partition: a dynamics-based framework for community detection. In:","volume-title":"Dynamics On and Of Complex Networks","author":"Delvenne,","year":"2013"},{"key":"key\n\t\t\t\t20180321100315_B2","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.physrep.2009.11.002","article-title":"Community detection in graphs.","volume":"486","author":"Fortunato,","year":"2010","journal-title":"Phys. Rep."},{"key":"key\n\t\t\t\t20180321100315_B3","doi-asserted-by":"crossref","first-page":"7821","DOI":"10.1073\/pnas.122653799","article-title":"Community structure in social and biological networks.","volume":"99","author":"Girvan,","year":"2002","journal-title":"Proc. Nat. Acad. Sci."},{"key":"key\n\t\t\t\t20180321100315_B4","first-page":"1082","article-title":"Communities in networks.","volume":"56","author":"Porter,","year":"2009","journal-title":"Not. AMS."},{"key":"key\n\t\t\t\t20180321100315_B5","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":"key\n\t\t\t\t20180321100315_B6","doi-asserted-by":"crossref","first-page":"052315","DOI":"10.1103\/PhysRevE.94.052315","article-title":"Equivalence between modularity optimization and maximum likelihood methods for community detection.","volume":"94","author":"Newman,","year":"2016","journal-title":"Phys. Rev. E."},{"key":"key\n\t\t\t\t20180321100315_B7","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1073\/pnas.0605965104","article-title":"Resolution limit in community detection.","volume":"104","author":"Fortunato,","year":"2007","journal-title":"Proc. Nat. Acad. Sci."},{"key":"key\n\t\t\t\t20180321100315_B8","doi-asserted-by":"crossref","first-page":"e32210","DOI":"10.1371\/journal.pone.0032210","article-title":"Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit.","volume":"7","author":"Schaub,","year":"2012","journal-title":"PLoS One"},{"key":"key\n\t\t\t\t20180321100315_B9","doi-asserted-by":"crossref","first-page":"12755","DOI":"10.1073\/pnas.0903215107","article-title":"Stability of graph communities across time scales.","volume":"107","author":"Delvenne,","year":"2010","journal-title":"Proc. Nat. Acad. Sci."},{"key":"key\n\t\t\t\t20180321100315_B10","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/TNSE.2015.2391998","article-title":"Random walks, Markov processes and the multiscale modular organization of complex networks.","volume":"1","author":"Lambiotte,","year":"2014","journal-title":"IEEE Trans. Network Sci. Eng"},{"key":"key\n\t\t\t\t20180321100315_B11","doi-asserted-by":"crossref","first-page":"2247","DOI":"10.1039\/C4MB00088A","article-title":"Uncovering allosteric pathways in caspase-1 using Markov transient analysis and multiscale community detection.","volume":"10","author":"Amor,","year":"2014","journal-title":"Mol. BioSyst."},{"key":"key\n\t\t\t\t20180321100315_B12","doi-asserted-by":"crossref","first-page":"055010","DOI":"10.1088\/1478-3975\/8\/5\/055010","article-title":"Protein multi-scale organization through graph partitioning and robustness analysis: application to the myosin\u2013myosin light chain interaction.","volume":"8","author":"Delmotte,","year":"2011","journal-title":"Phys. Biol."},{"key":"key\n\t\t\t\t20180321100315_B13","doi-asserted-by":"crossref","first-page":"20140940","DOI":"10.1098\/rsif.2014.0940","article-title":"Interest communities and flow roles in directed networks: the Twitter network of the UK riots.","volume":"11","author":"Beguerisse-D\u00edaz,","year":"2014","journal-title":"J. Roy. Soc. Interface"},{"key":"key\n\t\t\t\t20180321100315_B14","doi-asserted-by":"crossref","first-page":"e1005055","DOI":"10.1371\/journal.pcbi.1005055","article-title":"Flow-based network analysis of the Caenorhabditis elegans connectome.","volume":"12","author":"Bacik,","year":"2016","journal-title":"PLoS Comput Biol"},{"key":"key\n\t\t\t\t20180321100315_B15","doi-asserted-by":"crossref","first-page":"042822","DOI":"10.1103\/PhysRevE.88.042822","article-title":"Spectral methods for community detection and graph partitioning.","volume":"88,","author":"Newman,","year":"2013","journal-title":"Phys. Rev. E."},{"key":"key\n\t\t\t\t20180321100315_B16","doi-asserted-by":"crossref","first-page":"8577","DOI":"10.1073\/pnas.0601602103","article-title":"Modularity and community structure in networks.","volume":"103","author":"Newman,","year":"2006","journal-title":"Proc. Nat. Acad. Sci."},{"key":"key\n\t\t\t\t20180321100315_B17","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1002\/j.1538-7305.1970.tb01770.x","article-title":"An efficient heuristic procedure for partitioning graphs.","volume":"49","author":"Kernighan,","year":"1970","journal-title":"Bell Syst. Tech. J."},{"key":"key\n\t\t\t\t20180321100315_B18","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":"Stat. Comput."},{"key":"key\n\t\t\t\t20180321100315_B19","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1109\/34.868688","article-title":"Normalized cuts and image segmentation.","volume":"22","author":"Shi,","year":"2000","journal-title":"IEEE Trans Pattern Anal. Mach. Intell."},{"key":"key\n\t\t\t\t20180321100315_B20","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1109\/43.159993","article-title":"New spectral methods for ratio cut partitioning and clustering.","volume":"11","author":"Hagen,","year":"1992","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst"},{"key":"key\n\t\t\t\t20180321100315_B21","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1137\/1.9781611972757.25","article-title":"A spectral clustering approach to finding communities in graphs. In:","volume-title":"Proceedings of the 2005 SIAM International Conference on Data Mining","author":"White,","year":"2005"},{"key":"key\n\t\t\t\t20180321100315_B22","first-page":"195","article-title":"Spectral partitioning: the more eigenvectors, the better. In:","volume-title":"Proceedings of the 32nd annual ACM\/IEEE Design Automation Conference","author":"Alpert,","year":"1995"},{"key":"key\n\t\t\t\t20180321100315_B23","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1287\/moor.26.3.583.10587","article-title":"The vector partition problem for convex objective functions.","volume":"26","author":"Onn,","year":"2001","journal-title":"Math. Oper. Res."},{"key":"key\n\t\t\t\t20180321100315_B24","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. Theory Exp."},{"key":"key\n\t\t\t\t20180321100315_B25","doi-asserted-by":"crossref","first-page":"016110","DOI":"10.1103\/PhysRevE.74.016110","article-title":"Statistical mechanics of community detection.","volume":"74,","author":"Reichardt,","year":"2006","journal-title":"Phys. Rev. E."},{"key":"key\n\t\t\t\t20180321100315_B26","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0166-218X(98)00083-3","article-title":"Spectral partitioning with multiple eigenvectors.","volume":"90","author":"Alpert,","year":"1999","journal-title":"Discrete Appl. Math."},{"key":"key\n\t\t\t\t20180321100315_B27","doi-asserted-by":"crossref","first-page":"052808","DOI":"10.1103\/PhysRevE.92.052808","article-title":"Multiway spectral community detection in networks.","volume":"92,","author":"Zhang,","year":"2015","journal-title":"Phys. Rev. E."},{"key":"key\n\t\t\t\t20180321100315_B28","volume-title":"Linear Algebra and Geometry","author":"Shafarevich,","year":"2012"},{"key":"key\n\t\t\t\t20180321100315_B29","doi-asserted-by":"crossref","first-page":"2746","DOI":"10.1016\/j.camwa.2007.10.028","article-title":"A vector partitioning approach to detecting community structure in complex networks.","volume":"55","author":"Wang,","year":"2008","journal-title":"Comput. Math. Appl."},{"key":"key\n\t\t\t\t20180321100315_B30","doi-asserted-by":"crossref","first-page":"046110","DOI":"10.1103\/PhysRevE.78.046110","article-title":"Benchmark graphs for testing community detection algorithms.","volume":"78,","author":"Lancichinetti,","year":"2008","journal-title":"Phys. Rev. E."},{"key":"key\n\t\t\t\t20180321100315_B31","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":"key\n\t\t\t\t20180321100315_B32","first-page":"583","article-title":"Cluster ensembles\u2014a knowledge reuse framework for combining multiple partitions.","volume":"3","author":"Strehl,","year":"2002","journal-title":"J. Mach. Learn. Res."},{"key":"key\n\t\t\t\t20180321100315_B33","doi-asserted-by":"crossref","first-page":"016108","DOI":"10.1103\/PhysRevE.84.016108","article-title":"Penalized versions of the Newman\u2013Girvan modularity and their relation to normalized cuts and k-means clustering.","volume":"84,","author":"Bolla,","year":"2011","journal-title":"Phys. Rev. E"},{"key":"key\n\t\t\t\t20180321100315_B34","volume-title":"The Art of Scientific Computing. Numerical Recipes","author":"Press,","year":"2007","edition":"3rd edn"},{"key":"key\n\t\t\t\t20180321100315_B35","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4175.001.0001","volume-title":"Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond","author":"Scholkopf,","year":"2001"},{"key":"key\n\t\t\t\t20180321100315_B36","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.acha.2006.04.006","article-title":"Diffusion maps.","volume":"21","author":"Coifman,","year":"2006","journal-title":"Lect. Notes Appl. Numer. Harmon. Anal."},{"key":"key\n\t\t\t\t20180321100315_B37","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1109\/TKDE.2007.46","article-title":"Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation.","volume":"19","author":"Fouss,","year":"2007","journal-title":"IEEE Trans. Knowl. Data Eng."}],"container-title":["Journal of Complex Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/comnet\/article-pdf\/6\/2\/157\/24452295\/cnx028.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T00:25:12Z","timestamp":1750465512000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comnet\/article\/6\/2\/157\/4037125"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,26]]},"references-count":37,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,7,26]]},"published-print":{"date-parts":[[2018,4,1]]}},"URL":"https:\/\/doi.org\/10.1093\/comnet\/cnx028","relation":{},"ISSN":["2051-1310","2051-1329"],"issn-type":[{"value":"2051-1310","type":"print"},{"value":"2051-1329","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2018,4]]},"published":{"date-parts":[[2017,7,26]]}}}