In network theory, multidimensional networks, a special type of multilayer network, are networks with multiple kinds of relations.[1][2][3][4][5][6][7] Increasingly sophisticated attempts to model real-world systems as multidimensional networks have yielded valuable insight in the fields of social network analysis,[3][4][8][9][10][11][12] economics, urban and international transport,[13][14][15] ecology,[16][17][18][19] psychology,[20][21] medicine, biology,[22] commerce, climatology, physics,[23] computational neuroscience,[24][25][26][27] operations management, and finance.
^De Domenico, Manlio (2023-08-28). "More is different in real-world multilayer networks". Nature Physics. 19 (9). Springer Science and Business Media LLC: 1247–1262. Bibcode:2023NatPh..19.1247D. doi:10.1038/s41567-023-02132-1. ISSN 1745-2473. S2CID 261322676.
^Coscia, Michele; Rossetti, Giulio; Pennacchioli, Diego; Ceccarelli, Damiano; Giannotti, Fosca (2013). ""You know because I know": A multidimensional network approach to human resources problem". Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining. Advances in Social Network Analysis and Mining (ASONAM). Vol. 2013. pp. 434–441. arXiv:1305.7146. doi:10.1145/2492517.2492537. ISBN 9781450322409. S2CID 1810575.
^ abDe Domenico, M.; Solé-Ribalta, A.; Cozzo, E.; Kivelä, M.; Moreno, Y.; Porter, M.; Gómez, S.; Arenas, A. (2013). "Mathematical Formulation of Multilayer Networks" (PDF). Physical Review X. 3 (4): 041022. arXiv:1307.4977. Bibcode:2013PhRvX...3d1022D. doi:10.1103/PhysRevX.3.041022. S2CID 16611157. Archived from the original (PDF) on 2014-02-25. Retrieved 2016-02-13.
^ abBattiston, F.; Nicosia, V.; Latora, V. (2014). "Structural measures for multiplex networks". Physical Review E. 89 (3): 032804. arXiv:1308.3182. Bibcode:2014PhRvE..89c2804B. doi:10.1103/PhysRevE.89.032804. PMID 24730896. S2CID 13931603.
^Kivela, M.; Arenas, A.; Barthelemy, M.; Gleeson, J. P.; Moreno, Y.; Porter, M. A. (2014). "Multilayer networks". Journal of Complex Networks. 2 (3): 203–271. arXiv:1309.7233. doi:10.1093/comnet/cnu016. S2CID 11390956.
^Boccaletti, S.; Bianconi, G.; Criado, R.; del Genio, C. I.; Gómez-Gardeñes, J.; Romance, M.; Sendiña-Nadal, I.; Wang, Z.; Zanin, M. (2014). "The structure and dynamics of multilayer networks". Physics Reports. 544 (1): 1–122. arXiv:1407.0742. Bibcode:2014PhR...544....1B. doi:10.1016/j.physrep.2014.07.001. PMC 7332224. PMID 32834429.
^Battiston, Federico; Nicosia, Vincenzo; Latora, Vito (2017-02-01). "The new challenges of multiplex networks: Measures and models". The European Physical Journal Special Topics. 226 (3): 401–416. arXiv:1606.09221. Bibcode:2017EPJST.226..401B. doi:10.1140/epjst/e2016-60274-8. ISSN 1951-6355. S2CID 7205907.
^Mucha, P.; et al. (2010). "Community structure in time-dependent, multiscale, and multiplex networks" (PDF). Science. 328 (5980): 876–878. arXiv:0911.1824. Bibcode:2010Sci...328..876M. CiteSeerX 10.1.1.749.3504. doi:10.1126/science.1184819. PMID 20466926. S2CID 10920772.
^De Domenico, M.; Lancichinetti, A.; Arenas, A.; Rosvall, M. (2015). "Identifying Modular Flows on Multilayer Networks Reveals Highly Overlapping Organization in Interconnected Systems". Physical Review X. 5 (1): 011027. arXiv:1408.2925. Bibcode:2015PhRvX...5a1027D. doi:10.1103/PhysRevX.5.011027. S2CID 6364922.
^De Domenico, M.; Sole-Ribalta, A.; Omodei, E.; Gomez, S.; Arenas, A. (2015). "Ranking in interconnected multilayer networks reveals versatile nodes". Nature Communications. 6: 6868. arXiv:1311.2906. Bibcode:2015NatCo...6.6868D. doi:10.1038/ncomms7868. PMID 25904405.
^Rossi, Luca; Dickison, Mark E.; Magnani, Matteo (July 18, 2016). Multilayer Social Networks (1st ed.). Cambridge University Press.
^Cardillo, A.; et al. (2013). "Emergence of network features from multiplexity". Scientific Reports. 3: 1344. arXiv:1212.2153. Bibcode:2013NatSR...3E1344C. doi:10.1038/srep01344. PMC 3583169. PMID 23446838.
^Gallotti, R.; Barthelemy, M. (2014). "Anatomy and efficiency of urban multimodal mobility". Scientific Reports. 4: 6911. arXiv:1411.1274. Bibcode:2014NatSR...4E6911G. doi:10.1038/srep06911. PMC 4220282. PMID 25371238.
^De Domenico, M.; Sole-Ribalta, A.; Gomez, S.; Arenas, A. (2014). "Navigability of interconnected networks under random failures". PNAS. 111 (23): 8351–8356. Bibcode:2014PNAS..111.8351D. doi:10.1073/pnas.1318469111. PMC 4060702. PMID 24912174.
^Stella, M.; Andreazzi, C.S.; Selakovic, S.; Goudarzi, A.; Antonioni, A. (2016). "Parasite spreading in spatial ecological multiplex networks". Journal of Complex Networks. 5 (3): 486–511. arXiv:1602.06785. doi:10.1093/comnet/cnw028. S2CID 14398574.
^Pilosof, S.; Porter, M.A.; Pascual, M.; Kefi, S. (2017). "The Multilayer Nature of Ecological Networks". Nature Ecology & Evolution. 1 (4): 0101. arXiv:1511.04453. Bibcode:2017NatEE...1..101P. doi:10.1038/s41559-017-0101. PMID 28812678. S2CID 11387365.
^Timóteo, S.; Correia, M.; Rodríguez-Echeverría, S.; Freitas, H.; Heleno, R. (2018). "Multilayer networks reveal the spatial structure of seed-dispersal interactions across the Great Rift landscapes". Nature Communications. 9 (1): 140. Bibcode:2018NatCo...9..140T. doi:10.1038/s41467-017-02658-y. PMC 5762785. PMID 29321529.
^Costa, J.M.; Ramos, J.A.; Timóteo, S.; da Silva, L.P.; Ceia, R.C.; Heleno, R. (2018). "Species activity promote the stability of fruit-frugivore interactions across a five-year multilayer network". bioRxiv 10.1101/421941.
^Fiori, K. L.; Smith, J; Antonucci, T. C. (2007). "Social network types among older adults: A multidimensional approach". The Journals of Gerontology Series B: Psychological Sciences and Social Sciences. 62 (6): P322–30. doi:10.1093/geronb/62.6.p322. PMID 18079416.
^Stella, M.; Beckage, N. M.; Brede, M. (2017). "Multiplex lexical networks reveal patterns in early word acquisition in children". Scientific Reports. 21 (7): 619–23. arXiv:1609.03207. Bibcode:2017NatSR...746730S. doi:10.1038/srep46730. PMID 5402256. S2CID 13561769.
^De Domenico, M.; Nicosia, V.; Arenas, A.; Latora, V. (2015). "Structural reducibility of multilayer networks". Nature Communications. 6: 6864. arXiv:1405.0425. Bibcode:2015NatCo...6.6864D. doi:10.1038/ncomms7864. PMID 25904309.
^De Domenico, M.; Granell, C.; Porter, Mason A.; Arenas, A. (7 April 2016). "The physics of spreading processes in multilayer networks". Nature Physics. 12 (10): 901–906. arXiv:1604.02021. Bibcode:2016NatPh..12..901D. doi:10.1038/nphys3865. S2CID 5063264.
^Timme, N.; Ito, S.; Myroshnychenko, M.; Yeh, F.C.; Hiolski, E.; Hottowy, P.; Beggs, J.M. (2014). "Multiplex Networks of Cortical and Hippocampal Neurons Revealed at Different Timescales". PLOS ONE. 9 (12): e115764. Bibcode:2014PLoSO...9k5764T. doi:10.1371/journal.pone.0115764. PMC 4275261. PMID 25536059.
^De Domenico, M.; Sasai, S.; Arenas, A. (2016). "Mapping multiplex hubs in human functional brain networks". Frontiers in Neuroscience. 10: 326. arXiv:1603.05897. doi:10.3389/fnins.2016.00326. PMC 4945645. PMID 27471443.
^Battiston, F.; Nicosia, V.; Chavez, M.; Latora, V. (2017). "Multilayer motif analysis of brain networks". Chaos: An Interdisciplinary Journal of Nonlinear Science. 27 (4): 047404. arXiv:1606.09115. Bibcode:2017Chaos..27d7404B. doi:10.1063/1.4979282. PMID 28456158. S2CID 5206551.
^De Domenico, M. (2017). "Multilayer modeling and analysis of human brain networks". GigaScience. 6 (5): 1–8. doi:10.1093/gigascience/gix004. PMC 5437946. PMID 28327916.
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