{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T10:14:31Z","timestamp":1778580871879,"version":"3.51.4"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Netw Sci"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Complex networks are used as means for representing multimodal, real-life systems. With increasing amounts of data that lead to large multilayer networks consisting of different node and edge types, that can also be subject to temporal change, there is an increasing need for versatile visualization and analysis software. This work presents a lightweight Python library, Py3plex, which focuses on the visualization and analysis of multilayer networks. The library implements a set of simple graphical primitives supporting intra- as well as inter-layer visualization. It also supports many common operations on multilayer networks, such as aggregation, slicing, indexing, traversal, and more. The paper also focuses on how node embeddings can be used to speed up contemporary (multilayer) layout computation. The library\u2019s functionality is showcased on both real and synthetic networks.<\/jats:p>","DOI":"10.1007\/s41109-019-0203-7","type":"journal-article","created":{"date-parts":[[2019,10,30]],"date-time":"2019-10-30T22:23:13Z","timestamp":1572474193000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Py3plex toolkit for visualization and analysis of multilayer networks"],"prefix":"10.1007","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9916-8756","authenticated-orcid":false,"given":"Bla\u017e","family":"\u0160krlj","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Kralj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nada","family":"Lavra\u010d","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,10,29]]},"reference":[{"key":"203_CR1","doi-asserted-by":"crossref","unstructured":"Amato, R, Kouvaris NE, San Miguel M, D\u00edaz-Guilera A (2017) Opinion competition dynamics on multiplex networks. New J Phys 19(12).","DOI":"10.1088\/1367-2630\/aa936a"},{"key":"203_CR2","doi-asserted-by":"crossref","unstructured":"Auber, D, Archambault D, Bourqui R, Delest M, Dubois J, Lambert A, Mary P, Mathiaut M, M\u00e9lan\u00e7on G, Pinaud B, et al. (2017) TULIP 5. Springer.","DOI":"10.1007\/978-1-4614-7163-9_315-1"},{"key":"203_CR3","unstructured":"Auber, D (2004). In: J\u00fcnger M Mutzel P. (eds)Tulip \u2014 A Huge Graph Visualization Framework, 105\u2013126.. Springer, Berlin."},{"key":"203_CR4","doi-asserted-by":"crossref","unstructured":"Bastian, M, Heymann S, Jacomy M (2009) Gephi: an open source software for exploring and manipulating networks In: Third International AAAI Conference on Weblogs and Social Media.","DOI":"10.1609\/icwsm.v3i1.13937"},{"key":"203_CR5","doi-asserted-by":"crossref","unstructured":"Batagelj, V, Mrvar A (2001) Pajek\u2014analysis and visualization of large networks In: International Symposium on Graph Drawing, 477\u2013478.. Springer.","DOI":"10.1007\/3-540-45848-4_54"},{"issue":"10","key":"203_CR6","doi-asserted-by":"publisher","first-page":"10008","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 Stat Mech Theory Exp 2008(10):10008.","journal-title":"J Stat Mech Theory Exp"},{"issue":"1","key":"203_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2014.07.001","volume":"544","author":"S Boccaletti","year":"2014","unstructured":"Boccaletti, S, Bianconi G, Criado R, del Genio CI, G\u00f3mez-Garde\u00f1es J, Romance M, Sendi\u00f1a-Nadal I, Wang Z, Zanin M (2014) The structure and dynamics of multilayer networks. Phys Rep 544(1):1\u2013122.","journal-title":"Phys Rep"},{"key":"203_CR8","doi-asserted-by":"publisher","first-page":"6864","DOI":"10.1038\/ncomms7864","volume":"6","author":"M De Domenico","year":"2015","unstructured":"De Domenico, M, Nicosia V, Arenas A, Latora V (2015) Structural reducibility of multilayer networks. Nat Commun 6:6864.","journal-title":"Nat Commun"},{"issue":"2","key":"203_CR9","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1093\/comnet\/cnu038","volume":"3","author":"M De Domenico","year":"2015","unstructured":"De Domenico, M, Porter MA, Arenas A (2015) MuxViz: A tool for multilayer analysis and visualization of networks. J Complex Netw 3(2):159\u2013176.","journal-title":"J Complex Netw"},{"key":"203_CR10","doi-asserted-by":"publisher","unstructured":"De Domenico, M, Sol\u00e9-Ribalta A, Cozzo E, Kivel\u00e4 M, Moreno Y, Porter MA, G\u00f3mez S, Arenas A (2013) Mathematical formulation of multilayer networks. Phys Rev X 3(4). https:\/\/doi.org\/10.1103\/physrevx.3.041022 .","DOI":"10.1103\/physrevx.3.041022"},{"key":"203_CR11","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.knosys.2018.03.022","volume":"151","author":"P Goyal","year":"2018","unstructured":"Goyal, P, Ferrara E (2018) Graph embedding techniques, applications, and performance: A survey. Knowl-Based Syst 151:78\u201394.","journal-title":"Knowl-Based Syst"},{"key":"203_CR12","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1145\/2939672.2939754","volume-title":"Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201916","author":"A Grover","year":"2016","unstructured":"Grover, A, Leskovec J (2016) Node2vec: Scalable feature learning for networks In: Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201916, 855\u2013864.. ACM, New York."},{"key":"203_CR13","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/11618058_22","volume-title":"Graph Drawing","author":"S Hachul","year":"2006","unstructured":"Hachul, S, J\u00fcnger M (2006) An experimental comparison of fast algorithms for drawing general large graphs. In: Healy P Nikolov NS (eds)Graph Drawing, 235\u2013250.. Springer, Berlin, Heidelberg."},{"key":"203_CR14","unstructured":"Hagberg, A, Swart P, S Chult D (2008) Exploring network structure, dynamics, and function using NetworkX In: Proceedings of the 7th Python in Science Conference (SciPy)."},{"key":"203_CR15","doi-asserted-by":"crossref","unstructured":"Harel, D, Koren Y (2002) Graph drawing by high-dimensional embedding In: International Symposium on Graph Drawing, 207\u2013219.. Springer.","DOI":"10.1007\/3-540-36151-0_20"},{"issue":"2","key":"203_CR16","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/0378-8733(83)90021-7","volume":"5","author":"PW Holland","year":"1983","unstructured":"Holland, PW, Laskey KB, Leinhardt S (1983) Stochastic blockmodels: First steps. Soc Networks 5(2):109\u2013137.","journal-title":"Soc Networks"},{"issue":"3","key":"203_CR17","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1057\/ivs.2009.10","volume":"8","author":"W Huang","year":"2009","unstructured":"Huang, W, Eades P, Hong S-H (2009) Measuring effectiveness of graph visualizations: A cognitive load perspective. Inf Vis 8(3):139\u2013152.","journal-title":"Inf Vis"},{"issue":"3","key":"203_CR18","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1109\/MCSE.2007.55","volume":"9","author":"JD Hunter","year":"2007","unstructured":"Hunter, JD (2007) Matplotlib: A 2d graphics environment. Comput Sci Eng 9(3):90.","journal-title":"Comput Sci Eng"},{"issue":"6","key":"203_CR19","doi-asserted-by":"publisher","first-page":"98679","DOI":"10.1371\/journal.pone.0098679","volume":"9","author":"M Jacomy","year":"2014","unstructured":"Jacomy, M, Venturini T, Heymann S, Bastian M (2014) ForceAtlas2, A continuous graph algorithm for handy network visualization designed for the Gephi software. PloS ONE 9(6):98679.","journal-title":"PloS ONE"},{"key":"203_CR20","unstructured":"Jones, E, Oliphant T, Peterson P, et al (2001) SciPy: Open source scientific tools for Python."},{"issue":"3","key":"203_CR21","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1093\/comnet\/cnu016","volume":"2","author":"M Kivel\u00e4","year":"2014","unstructured":"Kivel\u00e4, M, Arenas A, Barthelemy M, Gleeson JP, Moreno Y, Porter MA (2014) Multilayer networks. J Complex Netw 2(3):203\u2013271.","journal-title":"J Complex Netw"},{"issue":"1","key":"203_CR22","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","volume":"22","author":"S Kullback","year":"1951","unstructured":"Kullback, S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79\u201386.","journal-title":"Ann Math Stat"},{"issue":"1","key":"203_CR23","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10844-017-0444-9","volume":"50","author":"J Kralj","year":"2018","unstructured":"Kralj, J, Robnik-\u0160ikonja M, Lavra\u010d N (2018) HINMINE: Heterogeneous Information Network Mining with Information Retrieval Heuristics. J Intell Inf Syst 50(1):29\u201361.","journal-title":"J Intell Inf Syst"},{"issue":"32","key":"203_CR24","first-page":"1","volume":"20","author":"J Kralj","year":"2019","unstructured":"Kralj, J, Robnik-Sikonja M, Lavrac N (2019) Netsdm: Semantic data mining with network analysis. J Mach Learn Res 20(32):1\u201350.","journal-title":"J Mach Learn Res"},{"issue":"1","key":"203_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2898361","volume":"8","author":"J Leskovec","year":"2016","unstructured":"Leskovec, J, Sosi\u010d R (2016) Snap: A general-purpose network analysis and graph-mining library. ACM Trans Intell Syst Technol 8(1):1\u20131120.","journal-title":"ACM Trans Intell Syst Technol"},{"issue":"Nov","key":"203_CR26","first-page":"2579","volume":"9","author":"Lvd Maaten","year":"2008","unstructured":"Maaten, Lvd, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9(Nov):2579\u20132605.","journal-title":"J Mach Learn Res"},{"key":"203_CR27","doi-asserted-by":"publisher","unstructured":"McGee, F, Ghoniem M, Melan\u00e7on G, Otjacques B, Pinaud B (2019) The state of the art in multilayer network visualization. Comput Graph Forum 0(0). https:\/\/doi.org\/10.1111\/cgf.13610 .","DOI":"10.1111\/cgf.13610"},{"key":"203_CR28","unstructured":"McInnes, L, Healy J, Melville J (2018) Umap: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426."},{"issue":"5","key":"203_CR29","first-page":"1","volume":"1695","author":"G Nepusz","year":"2006","unstructured":"Nepusz, G, Cs\u00e1rdi G (2006) The igraph software package for complex network research. Complex Syst 1695(5):1\u20139.","journal-title":"Complex Syst"},{"key":"203_CR30","doi-asserted-by":"publisher","first-page":"59","DOI":"10.3389\/fphy.2015.00059","volume":"3","author":"E Omodei","year":"2015","unstructured":"Omodei, E, De Domenico MD, Arenas A (2015) Characterizing interactions in online social networks during exceptional events. Front Phys 3:59.","journal-title":"Front Phys"},{"issue":"D1","key":"203_CR31","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1093\/nar\/gkt1115","volume":"42","author":"S Orchard","year":"2013","unstructured":"Orchard, S, Ammari M, Aranda B, Breuza L, Briganti L, Broackes-Carter F, Campbell NH, Chavali G, Chen C, Del-Toro N, et al (2013) The mintact project\u2014intact as a common curation platform for 11 molecular interaction databases. Nucleic Acids Res 42(D1):358\u2013363.","journal-title":"Nucleic Acids Res"},{"issue":"1","key":"203_CR32","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1186\/1752-0509-2-104","volume":"2","author":"GA Pavlopoulos","year":"2008","unstructured":"Pavlopoulos, GA, O\u2019Donoghue SI, Satagopam VP, Soldatos TG, Pafilis E, Schneider R (2008) Arena3d: visualization of biological networks in 3d. BMC Syst Biol 2(1):104.","journal-title":"BMC Syst Biol"},{"key":"203_CR33","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1145\/2623330.2623732","volume-title":"Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201914","author":"B Perozzi","year":"2014","unstructured":"Perozzi, B, Al-Rfou R, Skiena S (2014) Deepwalk: Online learning of social representations In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201914, 701\u2013710.. ACM, New York."},{"key":"203_CR34","doi-asserted-by":"crossref","unstructured":"Purchase, H (1997) Which aesthetic has the greatest effect on human understanding? In: International Symposium on Graph Drawing, 248\u2013261.. Springer.","DOI":"10.1007\/3-540-63938-1_67"},{"key":"203_CR35","unstructured":"Renoust, B, Melan\u00e7on G, Viaud M-L (2014). In: Missaoui R Sarr I (eds)Entanglement in Multiplex Networks: Understanding Group Cohesion in Homophily Networks, 89\u2013117.. Springer, Cham."},{"key":"203_CR36","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1145\/3097983.3098061","volume-title":"Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201917","author":"LFR Ribeiro","year":"2017","unstructured":"Ribeiro, LFR, Saverese PHP, Figueiredo DR (2017) Struc2vec: Learning node representations from structural identity In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD \u201917, 385\u2013394.. ACM, New York."},{"issue":"1","key":"203_CR37","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1140\/epjst\/e2010-01179-1","volume":"178","author":"M Rosvall","year":"2009","unstructured":"Rosvall, M, Axelsson D, Bergstrom CT (2009) The map equation. Eur Phys J Spec Top 178(1):13\u201323.","journal-title":"Eur Phys J Spec Top"},{"issue":"1","key":"203_CR38","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1186\/1471-2105-13-45","volume":"13","author":"M Secrier","year":"2012","unstructured":"Secrier, M, Pavlopoulos GA, Aerts J, Schneider R (2012) Arena3d: visualizing time-driven phenotypic differences in biological systems. BMC Bioinformatics 13(1):45.","journal-title":"BMC Bioinformatics"},{"issue":"11","key":"203_CR39","doi-asserted-by":"publisher","first-page":"2498","DOI":"10.1101\/gr.1239303","volume":"13","author":"P Shannon","year":"2003","unstructured":"Shannon, P (2003) Cytoscape: A software environment for integrated models of biomolecular interaction networks. Genome Res 13(11):2498\u20132504.","journal-title":"Genome Res"},{"key":"203_CR40","doi-asserted-by":"publisher","unstructured":"\u0160krlj, B, Kralj J, Lavra\u010d N (2019) Cbssd: community-based semantic subgroup discovery. J Intell Inf Syst. https:\/\/doi.org\/10.1007\/s10844-019-00545-0 .","DOI":"10.1007\/s10844-019-00545-0"},{"key":"203_CR41","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1007\/978-3-319-78680-3_13","volume-title":"New Frontiers in Mining Complex Patterns","author":"B \u0160krlj","year":"2018","unstructured":"\u0160krlj, B, Kralj J, Vavpeti\u010d A, Lavra\u010d N (2018) Community-based semantic subgroup discovery. In: Appice A, Loglisci C, Manco G, Masciari E, Ras ZW (eds)New Frontiers in Mining Complex Patterns, 182\u2013196.. Springer, Cham."},{"key":"203_CR42","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1007\/978-3-030-05411-3_60","volume-title":"Complex Networks and Their Applications VII","author":"B \u0160krlj","year":"2019","unstructured":"\u0160krlj, B, Kralj J, Lavra\u010d N (2019) Py3plex: A library for scalable multilayer network analysis and visualization. In: Aiello LM, Cherifi C, Cherifi H, Lambiotte R, Li\u00f3 P, Rocha LM (eds)Complex Networks and Their Applications VII, 757\u2013768.. Springer, Cham."},{"key":"203_CR43","unstructured":"Smilkov, D, Thorat N, Nicholson C, Reif E, Vi\u00e9gas FB, Wattenberg M (2016) Embedding projector: Interactive visualization and interpretation of embeddings. arXiv preprint arXiv:1611.05469."},{"key":"203_CR44","volume-title":"User Guide and Reference Manual","author":"The Boost Graph Library","year":"2002","unstructured":"The Boost Graph Library (2002) User Guide and Reference Manual. Addison-Wesley Longman Publishing Co., Inc., Boston."},{"issue":"2","key":"203_CR45","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1109\/MCSE.2011.37","volume":"13","author":"Svd Walt","year":"2011","unstructured":"Walt, Svd, Colbert SC, Varoquaux G (2011) The numpy array: a structure for efficient numerical computation. Comput Sci Eng 13(2):22\u201330.","journal-title":"Comput Sci Eng"},{"issue":"5","key":"203_CR46","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1140\/epjb\/e2015-60270-7","volume":"88","author":"Z Wang","year":"2015","unstructured":"Wang, Z, Wang L, Szolnoki A, Perc M (2015) Evolutionary games on multilayer networks: a colloquium. Eur Phys J B 88(5):124.","journal-title":"Eur Phys J B"},{"issue":"14","key":"203_CR47","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1093\/bioinformatics\/btx252","volume":"33","author":"M Zitnik","year":"2017","unstructured":"Zitnik, M, Leskovec J (2017) Predicting multicellular function through multi-layer tissue networks. Bioinformatics 33(14):190\u2013198.","journal-title":"Bioinformatics"}],"container-title":["Applied Network Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s41109-019-0203-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s41109-019-0203-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s41109-019-0203-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T08:55:46Z","timestamp":1695372946000},"score":1,"resource":{"primary":{"URL":"https:\/\/appliednetsci.springeropen.com\/articles\/10.1007\/s41109-019-0203-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,29]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["203"],"URL":"https:\/\/doi.org\/10.1007\/s41109-019-0203-7","relation":{},"ISSN":["2364-8228"],"issn-type":[{"value":"2364-8228","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,29]]},"assertion":[{"value":"9 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 August 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 October 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"94"}}