Agarwal G, Kempe D (2008) Modularity-maximizing graph communities via mathematical programming. Eur Phys J B 66(3):409–418. https://doi.org/10.1140/epjb/e2008-00425-1

Article
MathSciNet
MATH
Google Scholar

Aldecoa R, Marìn I (2011) Deciphering network community structure by surprise. PLoS one 6(9):e24195. https://doi.org/10.1371/journal.pone.0024195

Article
Google Scholar

Aloise D, Cafieri S, Caporossi G, Hansen P, Perron S, Liberti L (2010) Column generation algorithms for exact modularity maximization in networks. Phys Rev E 82(4):46112. https://doi.org/10.1103/PhysRevE.82.046112

Article
Google Scholar

Amini A, Kung K, Kang C, Sobolevsky S, Ratti C (2014) The impact of social segregation on human mobility in developing and industrialized regions. EPJ Data Sci 3(1):6

Article
Google Scholar

Baird D, Ulanowicz RE (1989) The seasonal dynamics of the Chesapeake Bay ecosystem. Ecol Monogr 59(4):329–364

Article
Google Scholar

Ball B, Karrer B, Newman MEJ (2011) Efficient and principled method for detecting communities in networks. Phys Rev E 84:036103. https://doi.org/10.1103/PhysRevE.84.036103

Article
Google Scholar

Belyi A, Bojic I, Sobolevsky S, Sitko I, Hawelka B, Rudikova L et al (2017) Global multi-layer network of human mobility. Int J Geogr Inf Sci 31(7):1381–1402

Article
Google Scholar

Belyi A, Sobolevsky S, Kurbatski A, Ratti C (2019) Improved upper bounds in clique partitioning problem. J Belarusian State Univ Math Inf 2019(3):93–104. https://doi.org/10.33581/2520-6508-2019-3-93-104

Article
Google Scholar

Bengio Y, Lodi A, Prouvost A (2021) Machine learning for combinatorial optimization: a methodological tour d’horizon. European J Oper Res 290(2):405–421. https://doi.org/10.1016/j.ejor.2020.07.063

Article
MathSciNet
MATH
Google Scholar

Bickel PJ, Chen A (2009) A nonparametric view of network models and Newman-Girvan and other modularities. Proceed Natl Acad Sci 106(50):21068–21073

Article
Google Scholar

Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp 2008(10):P10008

Article
Google Scholar

Bruna J, Li X (2017) Community detection with graph neural networks. Stat 1050:27

Google Scholar

Clauset A, Newman MEJ, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70:066111. https://doi.org/10.1103/PhysRevE.70.066111

Article
Google Scholar

Decelle A, Krzakala F, Moore C, Zdeborová L (2011) Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications. Phys Rev E 84:066106. https://doi.org/10.1103/PhysRevE.84.066106

Article
Google Scholar

Decelle A, Krzakala F, Moore C, Zdeborová L (2011) Inference and phase transitions in the detection of modules in sparse networks. Phys Rev Lett 107:065701. https://doi.org/10.1103/PhysRevLett.107.065701

Article
Google Scholar

Duch J, Arenas A (2005) Community detection in complex networks using extremal optimization. Phys Rev E 72:027104. https://doi.org/10.1103/PhysRevE.72.027104

Article
Google Scholar

Džamić D, Aloise D, Mladenović N (2019) Ascent-descent variable neighborhood decomposition search for community detection by modularity maximization. Ann Oper Res 272(1):273–287. https://doi.org/10.1007/s10479-017-2553-9

Article
MathSciNet
MATH
Google Scholar

Fortunato S (2010) Community detection in graphs. Phys Rep 486:75–174

Article
MathSciNet
Google Scholar

Fortunato S, Barthélémy M (2007) Resolution limit in community detection. Proceed Natl Acad Sci 104(1):36–41. https://doi.org/10.1073/pnas.0605965104

Article
Google Scholar

Fortunato S, Hric D (2016) Community detection in networks: a user guide. Phys Rep 659:1–44

Article
MathSciNet
Google Scholar

Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99(12):7821–7826

Article
MathSciNet
Google Scholar

Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proceed Natl Acad Sci 99(12):7821–7826. https://doi.org/10.1073/pnas.122653799

Article
MathSciNet
MATH
Google Scholar

Gleiser PM, Danon L (2003) Community structure in Jazz. Adv Complex Syst 06(04):565–573. https://doi.org/10.1142/S0219525903001067

Article
Google Scholar

Good BH, de Montjoye YA, Clauset A (2010) Performance of modularity maximization in practical contexts. Phys Rev E 81:046106. https://doi.org/10.1103/PhysRevE.81.046106

Article
MathSciNet
Google Scholar

Grauwin S, Szell M, Sobolevsky S, Hövel P, Simini F, Vanhoof M et al (2017) Identifying and modeling the structural discontinuities of human interactions. Sci Rep 7(1):1–11

Article
Google Scholar

Guimerà R, Nunes Amaral LA (2005) Functional cartography of complex metabolic networks. Nature 433(7028):895–900. https://doi.org/10.1038/nature03288

Article
Google Scholar

Guimerà R, Danon L, Díaz-Guilera A, Giralt F, Arenas A (2003) Self-similar community structure in a network of human interactions. Phys Rev E 68:065103. https://doi.org/10.1103/PhysRevE.68.065103

Article
Google Scholar

Guimera R, Sales-Pardo M, Amaral LAN (2004) Modularity from fluctuations in random graphs and complex networks. Phys Rev E 70(2):025101

Article
Google Scholar

Hamann M, Strasser B, Wagner D, Zeitz T (2018) Distributed graph clustering using modularity and map equation. In: Aldinucci M, Padovani L, Torquati M (eds) Euro-Par 2018: parallel processing. Springer International Publishing, Cham, pp 688–702

Chapter
Google Scholar

Hastie T (2001) The elements of statistical learning : data mining, inference, and prediction : with 200 full-color illustrations. Springer, New York

Google Scholar

Hawelka B, Sitko I, Beinat E, Sobolevsky S, Kazakopoulos P, Ratti C (2014) Geo-located Twitter as proxy for global mobility patterns. Cartogr Geogr Inf Sci 41(3):260–271

Article
Google Scholar

Holland PW, Laskey KB, Leinhardt S (1983) Stochastic blockmodels: first steps. Soc Networks 5(2):109–137

Article
MathSciNet
Google Scholar

Javed MA, Younis MS, Latif S, Qadir J, Baig A (2018) Community detection in networks: a multidisciplinary review. J Network Comput Appl 108:87–111

Article
Google Scholar

Kampffmeyer M, Løkse S, Bianchi FM, Livi L, Salberg AB, Jenssen R (2019) Deep divergence-based approach to clustering. Neural Networks 113:91–101. https://doi.org/10.1016/j.neunet.2019.01.015

Article
Google Scholar

Karrer B, Newman MEJ (2011) Stochastic blockmodels and community structure in networks. Phys Rev E 83:016107. https://doi.org/10.1103/PhysRevE.83.016107

Article
MathSciNet
Google Scholar

Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E 78(4):046110

Article
Google Scholar

Landsman D, Kats P, Nenko A, Sobolevsky S (2020) Zoning of St. Petersburg through the prism of social activity networks. Procedia Comput Sci 178:125–133

Article
Google Scholar

Lee J, Gross SP, Lee J (2012) Modularity optimization by conformational space annealing. Phys Rev E 85:056702. https://doi.org/10.1103/PhysRevE.85.056702

Article
Google Scholar

Liu X, Murata T (2010) Advanced modularity-specialized label propagation algorithm for detecting communities in networks. Phys A Stat Mech Appl 389(7):1493–1500. https://doi.org/10.1016/j.physa.2009.12.019

Article
Google Scholar

Lu H, Halappanavar M, Kalyanaraman A (2015) Parallel heuristics for scalable community detection. Parallel Comput 47:19–37. https://doi.org/10.1016/j.parco.2015.03.003

Article
MathSciNet
Google Scholar

Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten E, Dawson SM (2003) The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Behav Ecol Sociobiol 54(4):396–405. https://doi.org/10.1007/s00265-003-0651-y

Article
Google Scholar

Newman MEJ (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69:066133. https://doi.org/10.1103/PhysRevE.69.066133

Article
Google Scholar

Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74:036104. https://doi.org/10.1103/PhysRevE.74.036104

Article
MathSciNet
Google Scholar

Newman MEJ (2006) Modularity and community structure in networks. Proceed Nat Academ Sci 103(23):8577–8582

Article
Google Scholar

Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026113

Article
Google Scholar

Piccardi C, Tajoli L (2012) Existence and significance of communities in the World Trade Web. Phys Rev E. https://doi.org/10.1103/PhysRevE.85.066119

Article
Google Scholar

Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76:036106. https://doi.org/10.1103/PhysRevE.76.036106

Article
Google Scholar

Ratti C, Sobolevsky S, Calabrese F, Andris C, Reades J, Martino M et al (2010) Redrawing the Map of Great Britain from a Network of Human Interactions. PLoS one 5(12):e14248. https://doi.org/10.1371/journal.pone.0014248

Article
Google Scholar

Rossetti G, Milli L, Cazabet R (2019) CDLIB: a python library to extract, compare and evaluate communities from complex networks. Appl Network Sci 4(1):1–26. https://doi.org/10.1007/s41109-019-0165-9

Article
Google Scholar

Rosvall M, Bergstrom CT (2007) An information-theoretic framework for resolving community structure in complex networks. Proceed Natl Acad Sci 104(18):7327–7331. https://doi.org/10.1073/pnas.0611034104

Article
Google Scholar

Rosvall M, Bergstrom CT (2008) Maps of random walks on complex networks reveal community structure. Proc Natl Acad Sci USA 105:1118–1123

Article
Google Scholar

Sobolevsky S, Szell M, Campari R, Couronné T, Smoreda Z, Ratti C (2013) Delineating geographical regions with networks of human interactions in an extensive set of countries. PloS one 8(12):e81707

Article
Google Scholar

Sobolevsky S, Campari R, Belyi A, Ratti C (2014) General optimization technique for high-quality community detection in complex networks. Phys Rev E 90(1):012811

Article
Google Scholar

Traag VA, Waltman L, Van Eck NJ (2019) From Louvain to Leiden: guaranteeing well-connected communities. Sci Rep 9(1):1–12. https://doi.org/10.1038/s41598-019-41695-z

Article
Google Scholar

Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442

Article
Google Scholar

Weisfeiler B, Leman A (1968) The reduction of a graph to canonical form and the algebra which appears therein. NTI, Series 2(9):12–16

Google Scholar

White JG, Southgate E, Thomson JN, Brenner S (1986) The structure of the nervous system of the nematode caenorhabditis elegans. Philos Trans Royal Soc London B Biol Sci 314(1165):1–340. https://doi.org/10.1098/rstb.1986.0056

Article
Google Scholar

Xu Y, Li J, Belyi A, Park S (2021) Characterizing destination networks through mobility traces of international tourists - a case study using a nationwide mobile positioning dataset. Tour Manag. https://doi.org/10.1016/j.tourman.2020.104195

Article
Google Scholar

Yan X, Shalizi C, Jensen JE, Krzakala F, Moore C, Zdeborová L et al (2014) Model selection for degree-corrected block models. J Stat Mech Theory Exp 2014(5):P05007

Article
Google Scholar

Zachary WW (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33:452–473

Article
Google Scholar

Adamic LA, Glance N (2005) The political blogosphere and the 2004 U.S. election: divided they blog. In: Proceedings of the 3rd international workshop on Link discovery. LinkKDD ’05. New York, NY, USA: ACM; p 36–43. Available from: http://doi.acm.org/10.1145/1134271.1134277. https://doi.org/10.1145/1134271.1134277

Aloise D, Caporossi G, Hansen P, Liberti L, Perron S, Ruiz M (2012) Modularity maximization in networks by variable neighborhood search. Graph Partitioning and Graph Clustering. 588(113)

Bandyopadhyay S, Peter V (2020) Self-expressive graph neural network for unsupervised community detection. arXiv preprint arXiv:2011.14078

Barber MJ, Clark JW (2009) Detecting network communities by propagating labels under constraints. Phys Rev E. 80, 026129. https://doi.org/10.1103/PhysRevE.80.026129

Belyi A, Sobolevsky S (2022) Network Size Reduction Preserving Optimal Modularity and Clique Partition. In: Gervasi O, Murgante B, Hendrix EMT, Taniar D, Apduhan BO (eds). Computational science and its applications – ICCSA 2022. Cham: Springer International Publishing; p 19–33. https://doi.org/10.1007/978-3-031-10522-7_2

Belyi A, Sobolevsky S, Kurbatski A, Ratti C (2021) Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem. arXiv preprint arXiv:2110.05627

Bianchi FM (2022) Simplifying clustering with graph neural networks. arXiv preprint arXiv:2207.08779

Bianchi FM, Grattarola D, Alippi C (2020) Spectral Clustering with Graph Neural Networks for Graph Pooling. In: III HD, Singh A, editors. In: Proceedings of the 37th international conference on machine learning. vol. 119 of Proceedings of Machine Learning Research. PMLR; p 874–883. Available from: https://proceedings.mlr.press/v119/bianchi20a.html

Biedermann S, Henzinger M, Schulz C, Schuster B (2018) Memetic Graph Clustering. In: D’Angelo G, editor. 17th International Symposium on Experimental Algorithms (SEA 2018). vol. 103 of Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. p. 3:1–3:15. Available from: http://drops.dagstuhl.de/opus/volltexte/2018/8938. https://doi.org/10.4230/LIPIcs.SEA.2018.3

Blondel V, Krings G, Thomas I (2010) Regions and borders of mobile telephony in Belgium and in the Brussels metropolitan zone. Brussels Studies La revue scientifique électronique pour les recherches sur Bruxelles/Het elektronisch wetenschappelijk tijdschrift voor onderzoek over Brussel/The e-journal for academic research on Brussels

Boguñá M, Pastor-Satorras R, Díaz-Guilera A, Arenas A (2004 Nov) Models of social networks based on social distance attachment. Phys Rev E. 70:056122. https://doi.org/10.1103/PhysRevE.70.056122

Brandes U, Delling D, Gaertler M, Görke R, Hoefer M, Nikoloski Z, et al (2006) Maximizing modularity is hard. arXiv preprint physics/0608255

Chen Z, Li X, Bruna J (2017) Supervised community detection with line graph neural networks. arXiv preprint arXiv:1705.08415

Jung S, Keuper M (2022) Learning to solve minimum cost multicuts efficiently using edge-weighted graph convolutional neural networks. arXiv preprint arXiv:2204.01366

Kang C, Sobolevsky S, Liu Y, Ratti C (2013) Exploring human movements in Singapore: A comparative analysis based on mobile phone and taxicab usages. In: Proceedings of the 2nd ACM SIGKDD international workshop on urban computing. ACM; p 1

Khan BS, Niazi MA (2017) Network community detection: a review and visual survey. arXiv preprint arXiv:1708.00977

Knuth DE (1993) The Stanford GraphBase: a platform for combinatorial computing. Addison-Wesley; Available from: http://www-cs-staff.stanford.edu/~uno/sgb.html

Landsman D, Kats P, Nenko A, Kudinov S, Sobolevsky S (2021) Social activity networks shaping St. Petersburg. In: Proceedings of the 54th Hawaii international conference on system sciences; p 1149

Li Z, Chen Q, Koltun V (2018) Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search. In: Bengio S, Wallach H, Larochelle H, Grauman K, Cesa-Bianchi N, Garnett R (eds). Advances in neural information processing systems. vol 31. Curran Associates, Inc. p 1–10. Available from: https://proceedings.neurips.cc/paper/2018/file/8d3bba7425e7c98c50f52ca1b52d3735-Paper.pdf

Lobov I, Ivanov S (2019) Unsupervised community detection with modularity-based attention model. arXiv preprint arXiv:1905.10350

Ma Y, Guo Z, Ren Z, Tang J, Yin D (2020) Streaming graph neural networks. In: Proceedings of the 43rd international ACM SIGIR conference on research and development in information retrieval; p 719–728

Plantié M, Crampes M (2013) Survey on social community detection. In: Social media retrieval. Springer; p 65–85

Sanders P, Schulz C, Wagner D (2014) Benchmarking for graph clustering and partitioning. Encyclopedia of social network analysis and mining Springer

Shchur O, Günnemann S (2019) Overlapping community detection with graph neural networks. arXiv preprint arXiv:1909.12201

Sobolevsky S, Sitko I, Des Combes RT, Hawelka B, Arias JM, Ratti C (2014) Money on the move: Big data of bank card transactions as the new proxy for human mobility patterns and regional delineation. the case of residents and foreign visitors in spain. In: Big data (BigData Congress), 2014 IEEE international congress on. IEEE; p 136–143

Sobolevsky S, Belyi A, Ratti C (2017) Optimality of community structure in complex networks. arXiv preprint arXiv:1712.05110

Sobolevsky S, Kats P, Malinchik S, Hoffman M, Kettler B, Kontokosta C (2018) Twitter Connections Shaping New York City. In: Proceedings of the 51st Hawaii international conference on system sciences. p 1008–1016

Sun Y, Danila B, Josić K, Bassler KE (2009) Improved community structure detection using a modified fine-tuning strategy. EPL (Europhysics Letters). 86(2):28004. Available from: http://stacks.iop.org/0295-5075/86/i=2/a=28004

Tsitsulin A, Palowitch J, Perozzi B, Müller E (2020) Graph clustering with graph neural networks. arXiv preprint arXiv:2006.16904

Wu Z, Pan S, Chen F, Long G, Zhang C, Philip SY (2020) A comprehensive survey on graph neural networks. In: IEEE transactions on neural networks and learning systems

Yow KS, Luo S (2022) Learning-based approaches for graph problems: a survey. arXiv preprint arXiv:2204.01057