{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T03:50:50Z","timestamp":1770177050090,"version":"3.49.0"},"reference-count":86,"publisher":"Association for Computing Machinery (ACM)","issue":"7","funder":[{"DOI":"10.13039\/501100004359","name":"Swedish Research Council","doi-asserted-by":"crossref","award":["2016-00796"],"award-info":[{"award-number":["2016-00796"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"crossref"}]},{"name":"German Federal Ministry of Education and Research","award":["100582863"],"award-info":[{"award-number":["100582863"]}]},{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["176938"],"award-info":[{"award-number":["176938"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Swedish Foundation for Strategic Research","award":["SB16-0089"],"award-info":[{"award-number":["SB16-0089"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Comput. Surv."],"published-print":{"date-parts":[[2026,5,31]]},"abstract":"<jats:p>Real-world networks have a complex topology comprising many elements often structured into communities. Revealing these communities helps researchers uncover the organizational and functional structure of the system that the network represents. However, detecting community structures in complex networks requires selecting a community detection method among a multitude of alternatives with different network representations, community interpretations, and underlying mechanisms. This tutorial focuses on a popular community detection method called the map equation and its search algorithm Infomap. The map equation framework for community detection describes communities by analyzing dynamic processes on the network. Thanks to its flexibility, the map equation provides extensions that can incorporate various assumptions about network structure and dynamics. To help decide if the map equation is a suitable community detection method for a given complex system and problem at hand\u2014and which variant to choose\u2014we review the map equation\u2019s theoretical framework and guide users in applying the map equation to various research problems.<\/jats:p>","DOI":"10.1145\/3779648","type":"journal-article","created":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T14:17:12Z","timestamp":1765030632000},"page":"1-34","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Community Detection with the Map Equation and Infomap: Theory and Applications"],"prefix":"10.1145","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0124-1909","authenticated-orcid":false,"given":"Jelena","family":"Smiljani\u0107","sequence":"first","affiliation":[{"name":"IceLab, Department of Physics, Ume\u00e5 University","place":["Ume\u00e5, Sweden"]},{"name":"Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade","place":["Ume\u00e5, Sweden"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7881-2496","authenticated-orcid":false,"given":"Christopher","family":"Bl\u00f6cker","sequence":"additional","affiliation":[{"name":"IceLab, Department of Physics, Ume\u00e5 University","place":["Ume\u00e5, Sweden"]},{"name":"Center for Artificial Intelligence and Data Science, University of W\u00fcrzburg","place":["Ume\u00e5, Sweden"]},{"name":"Data Analytics Group, Department of Informatics, University of Z\u00fcrich","place":["Ume\u00e5, Sweden"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5859-4073","authenticated-orcid":false,"given":"Anton","family":"Holmgren","sequence":"additional","affiliation":[{"name":"IceLab, Department of Physics, Ume\u00e5 University","place":["Ume\u00e5, Sweden"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5420-0591","authenticated-orcid":false,"given":"Daniel","family":"Edler","sequence":"additional","affiliation":[{"name":"IceLab, Department of Physics, Ume\u00e5 University","place":["Ume\u00e5, Sweden"]},{"name":"Gothenburg Global Biodiversity Centre, University of Gothenburg","place":["Ume\u00e5, Sweden"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3599-9374","authenticated-orcid":false,"given":"Magnus","family":"Neuman","sequence":"additional","affiliation":[{"name":"IceLab, Department of Physics, Ume\u00e5 University","place":["Ume\u00e5, Sweden"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7181-9940","authenticated-orcid":false,"given":"Martin","family":"Rosvall","sequence":"additional","affiliation":[{"name":"IceLab, Department of Physics, Ume\u00e5 University","place":["Ume\u00e5, Sweden"]}]}],"member":"320","published-online":{"date-parts":[[2026,2,3]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep02216"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.062312"},{"key":"e_1_3_1_4_2","volume-title":"Network Science","author":"Barab\u00e1si Albert-L\u00e1szl\u00f3","year":"2016","unstructured":"Albert-L\u00e1szl\u00f3 Barab\u00e1si and M\u00e1rton P\u00f3sfai. 2016. Network Science. Cambridge University Press, Cambridge. Retrieved from http:\/\/barabasi.com\/networksciencebook\/"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abn7558"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2020.05.004"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-022-00477-9"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.052305"},{"key":"e_1_3_1_9_2","volume-title":"Proceedings of the 1st Learning on Graphs Conference","author":"Bl\u00f6cker Christopher","year":"2022","unstructured":"Christopher Bl\u00f6cker, Jelena Smiljani\u0107, Ingo Scholtes, and Martin Rosvall. 2022. Similarity-based link prediction from modular compression of network flows. In Proceedings of the 1st Learning on Graphs Conference."},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.52202\/079017-0554"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2008\/10\/P10008"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10377-8_1"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.052308"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.022308"},{"key":"e_1_3_1_15_2","first-page":"1172","volume-title":"Proceedings of the 36th International Conference on Machine Learning","author":"Chitra Uthsav","year":"2019","unstructured":"Uthsav Chitra and Benjamin Raphael. 2019. Random walks on hypergraphs with edge-dependent vertex weights. In Proceedings of the 36th International Conference on Machine Learning. PMLR, 1172\u20131181."},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.5.011027"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0903215107"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1111\/jbi.13190"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.3390\/a10040112"},{"issue":"2","key":"e_1_3_1_20_2","first-page":"197","article-title":"Infomap bioregions: Interactive mapping of biogeographical regions from species distributions","volume":"66","author":"Edler Daniel","year":"2017","unstructured":"Daniel Edler, Tha\u00eds Guedes, Alexander Zizka, Martin Rosvall, and Alexandre Antonelli. 2017. Infomap bioregions: Interactive mapping of biogeographical regions from species distributions. Systematic Biology 66, 2 (2017), 197\u2013204.","journal-title":"Systematic Biology"},{"key":"e_1_3_1_21_2","article-title":"The Infomap Python package","author":"Edler Daniel","year":"2020","unstructured":"Daniel Edler, Anton Holmgren, and Martin Rosvall. 2020. The Infomap Python package. Retrieved from https:\/\/mapequation.github.io\/infomap\/python\/","journal-title":"Retrieved from https:\/\/mapequation.github.io\/infomap\/python\/"},{"key":"e_1_3_1_22_2","article-title":"The MapEquation software package","author":"Edler Daniel","year":"2022","unstructured":"Daniel Edler, Anton Holmgren, and Martin Rosvall. 2022. The MapEquation software package. Retrieved from https:\/\/mapequation.org","journal-title":"Retrieved from https:\/\/mapequation.org"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","unstructured":"Daniel Edler Jelena Smiljani\u0107 Anton Holmgren Alexandre Antonelli and Martin Rosvall. 2022. Variable Markov dynamics as a multifocal lens to map multiscale complex networks. arXiv:2211.04287. Retrieved from 10.48550\/arXiv.2211.04287","DOI":"10.48550\/arXiv.2211.04287"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.022301"},{"key":"e_1_3_1_25_2","volume-title":"Interactive Visualization of Community Structure in Complex Networks","author":"Eriksson Anton","year":"2018","unstructured":"Anton Eriksson. 2018. Interactive Visualization of Community Structure in Complex Networks. Master\u2019s thesis. Department of Physics, Ume\u00e5 University. diva:1215352 Retrieved from http:\/\/urn.kb.se\/resolve?urn=urn%3Anbn%3Ase%3Aumu%3Adiva-148551diva2:1215352."},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-91374-8_4"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-021-00634-z"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","unstructured":"Alcides Viamontes Esquivel and Martin Rosvall. 2012. Comparing network covers using mutual information. arXiv:1202.0425. Retrieved from 10.48550\/arXiv.1202.0425","DOI":"10.48550\/arXiv.1202.0425"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1111\/2041-210X.13569"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1956-045-5"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2009.11.002"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0605965104"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.09.002"},{"key":"e_1_3_1_34_2","first-page":"1","article-title":"Evaluating overfit and underfit in models of network community structure","author":"Ghasemian Amir","year":"2019","unstructured":"Amir Ghasemian, Homa Hosseinmardi, and Aaron Clauset. 2019. Evaluating overfit and underfit in models of network community structure. IEEE Transactions on Knowledge and Data Engineering 9 (2019), 1\u20131.","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1137\/140976649"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219525903001067"},{"key":"e_1_3_1_37_2","article-title":"Matrix computations. 3rd edn the johns hopkins university press","author":"Golub Gene H.","year":"2008","unstructured":"Gene H. Golub and Charles F. Van Loan. 2008. Matrix computations. 3rd edn the johns hopkins university press. Baltimore, MD (2008).","journal-title":"Baltimore, MD"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.046106"},{"key":"e_1_3_1_39_2","doi-asserted-by":"publisher","DOI":"10.1145\/2939672.2939754"},{"key":"e_1_3_1_40_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1803908115"},{"key":"e_1_3_1_41_2","article-title":"Infomap Network Navigator","author":"Holmgren Anton","year":"2018","unstructured":"Anton Holmgren, Daniel Edler, and Martin Rosvall. 2018. Infomap Network Navigator. Retrieved from https:\/\/mapequation.org\/navigator","journal-title":"Retrieved from https:\/\/mapequation.org\/navigator"},{"key":"e_1_3_1_42_2","article-title":"Infomap Online","author":"Holmgren Anton","year":"2022","unstructured":"Anton Holmgren, Daniel Edler, and Martin Rosvall. 2022. Infomap Online. Retrieved from https:\/\/mapequation.org\/infomap","journal-title":"Retrieved from https:\/\/mapequation.org\/infomap"},{"key":"e_1_3_1_43_2","article-title":"The Map Equation Demo","author":"Holmgren Anton","year":"2022","unstructured":"Anton Holmgren, Daniel Edler, and Martin Rosvall. 2022. The Map Equation Demo. Retrieved from https:\/\/mapequation.org\/demo","journal-title":"https:\/\/mapequation.org\/demo"},{"key":"e_1_3_1_44_2","article-title":"The MapEquation Alluvial Diagram Generator","author":"Holmgren Anton","year":"2022","unstructured":"Anton Holmgren, Daniel Edler, and Martin Rosvall. 2022. The MapEquation Alluvial Diagram Generator. Retrieved from https:\/\/mapequation.org\/alluvial","journal-title":"Retrieved from https:\/\/mapequation.org\/alluvial"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-023-00572-5"},{"key":"e_1_3_1_46_2","doi-asserted-by":"publisher","DOI":"10.1109\/JRPROC.1952.273898"},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.91.012809"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.93.032309"},{"key":"e_1_3_1_49_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNSE.2015.2391998"},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.056107"},{"key":"e_1_3_1_51_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0459-y"},{"key":"e_1_3_1_52_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.056117"},{"key":"e_1_3_1_53_2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/11\/3\/033015"},{"key":"e_1_3_1_54_2","doi-asserted-by":"publisher","DOI":"10.1086\/261158"},{"key":"e_1_3_1_55_2","doi-asserted-by":"publisher","unstructured":"Maja Lindstr\u00f6m Rohit Sahasrabuddhe Anton Holmgren Christopher Bl\u00f6cker Tommy L\u00f6fstedt and Martin Rosvall. 2023. Mapping compact memory-biased dynamics reveals overlapping communities. arXiv:2304.05775. Retrieved from 10.48550\/arXiv.2304.05775","DOI":"10.48550\/arXiv.2304.05775"},{"key":"e_1_3_1_56_2","doi-asserted-by":"publisher","DOI":"10.21105\/joss.00861"},{"key":"e_1_3_1_57_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-024-00612-8"},{"key":"e_1_3_1_58_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-022-00516-5"},{"key":"e_1_3_1_59_2","doi-asserted-by":"publisher","unstructured":"Magnus Neuman Jelena Smiljani\u0107 and Martin Rosvall. 2025. Reliable data clustering with Bayesian community detection. arXiv:2510.15013. Retrieved from 10.48550\/arXiv.2510.15013","DOI":"10.48550\/arXiv.2510.15013"},{"key":"e_1_3_1_60_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.042304"},{"issue":"188","key":"e_1_3_1_61_2","first-page":"1","article-title":"Significance-based community detection in weighted networks","volume":"18","author":"Palowitch John","year":"2018","unstructured":"John Palowitch, Shankar Bhamidi, and Andrew B. Nobel. 2018. Significance-based community detection in weighted networks. Journal of Machine Learning Research 18, 188 (2018), 1\u201348.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_1_62_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1602548"},{"key":"e_1_3_1_63_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.110.148701"},{"key":"e_1_3_1_64_2","doi-asserted-by":"publisher","DOI":"10.1002\/9781119483298.ch11"},{"key":"e_1_3_1_65_2","doi-asserted-by":"publisher","unstructured":"Christian Persson Ludvig Bohlin Daniel Edler and Martin Rosvall. 2016. Maps of sparse Markov chains efficiently reveal community structure in network flows with memory. arXiv:1606.08328. Retrieved from 10.48550\/arXiv.1606.08328","DOI":"10.48550\/arXiv.1606.08328"},{"key":"e_1_3_1_66_2","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00124"},{"key":"e_1_3_1_67_2","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(78)90005-5"},{"key":"e_1_3_1_68_2","doi-asserted-by":"publisher","DOI":"10.1038\/s42003-021-01805-y"},{"key":"e_1_3_1_69_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-019-0165-9"},{"key":"e_1_3_1_70_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0706851105"},{"key":"e_1_3_1_71_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0008694"},{"key":"e_1_3_1_72_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0018209"},{"key":"e_1_3_1_73_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms5630"},{"key":"e_1_3_1_74_2","doi-asserted-by":"publisher","DOI":"10.1515\/dma.1995.5.6.515"},{"key":"e_1_3_1_75_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-017-0023-6"},{"key":"e_1_3_1_76_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0032210"},{"key":"e_1_3_1_77_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.026112"},{"key":"e_1_3_1_78_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"e_1_3_1_79_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.012302"},{"key":"e_1_3_1_80_2","doi-asserted-by":"publisher","DOI":"10.1093\/comnet\/cnab044"},{"key":"e_1_3_1_81_2","article-title":"vgraph: A generative model for joint community detection and node representation learning","volume":"32","author":"Sun Fan-Yun","year":"2019","unstructured":"Fan-Yun Sun, Meng Qu, Jordan Hoffmann, Chin-Wei Huang, and Jian Tang. 2019. vgraph: A generative model for joint community detection and node representation learning. Advances in Neural Information Processing Systems 32 (2019), 541\u2013524.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_1_82_2","doi-asserted-by":"publisher","DOI":"10.1137\/20M1355896"},{"key":"e_1_3_1_83_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-019-41695-z"},{"key":"e_1_3_1_84_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1961.tb02789.x"},{"key":"e_1_3_1_85_2","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2014.2364018"},{"key":"e_1_3_1_86_2","doi-asserted-by":"publisher","DOI":"10.1086\/jar.33.4.3629752"},{"key":"e_1_3_1_87_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0154404"}],"container-title":["ACM Computing Surveys"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3779648","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T14:19:01Z","timestamp":1770128341000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3779648"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,3]]},"references-count":86,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,5,31]]}},"alternative-id":["10.1145\/3779648"],"URL":"https:\/\/doi.org\/10.1145\/3779648","relation":{},"ISSN":["0360-0300","1557-7341"],"issn-type":[{"value":"0360-0300","type":"print"},{"value":"1557-7341","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,3]]},"assertion":[{"value":"2023-12-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-11-25","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-02-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}