{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T13:22:52Z","timestamp":1790169772253,"version":"4.1.0"},"reference-count":40,"publisher":"AIP Publishing","issue":"1","funder":[{"DOI":"10.13039\/100000183","name":"USARO","doi-asserted-by":"publisher","award":["W911NF-09-0001"],"award-info":[{"award-number":["W911NF-09-0001"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2014,3,1]]},"abstract":"<jats:p>We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of temporal network data in detail. In a network of coupled nonlinear oscillators, hyperedges that consist of network edges with temporally co-varying weights uncover the driving co-evolution patterns of edge weight dynamics both within and between oscillator communities. In the human brain, networks that represent temporal changes in brain activity during learning exhibit early co-evolution that then settles down with practice. Subsequent decreases in hyperedge size are consistent with emergence of an autonomous subgraph whose dynamics no longer depends on other parts of the network. Our results on real and synthetic networks give a poignant demonstration of the ability of cross-link structure to uncover unexpected co-evolution attributes in both real and synthetic dynamical systems. This, in turn, illustrates the utility of analyzing cross-links for investigating the structure of temporal networks.<\/jats:p>","DOI":"10.1063\/1.4858457","type":"journal-article","created":{"date-parts":[[2014,1,29]],"date-time":"2014-01-29T01:30:32Z","timestamp":1390959032000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":68,"title":["Cross-linked structure of network evolution"],"prefix":"10.1063","volume":"24","author":[{"given":"Danielle S.","family":"Bassett","sequence":"first","affiliation":[{"name":"Department of Bioengineering, University of Pennsylvania 1 , Philadelphia, Pennsylvania 19104, USA"},{"name":"Department of Physics, University of California 2 , Santa Barbara, California 93106, USA"},{"name":"Sage Center for the Study of the Mind, University of California 3 , Santa Barbara, California 93106, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicholas F.","family":"Wymbs","sequence":"additional","affiliation":[{"name":"Department of Psychology and UCSB Brain Imaging Center, University of California 4 , Santa Barbara, California 93106, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mason A.","family":"Porter","sequence":"additional","affiliation":[{"name":"Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford 5 , Oxford OX2 6GG, United Kingdom"},{"name":"CABDyN Complexity Centre, University of Oxford 6 , Oxford, OX1 1HP, United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter J.","family":"Mucha","sequence":"additional","affiliation":[{"name":"Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina 7 , Chapel Hill, North Carolina 27599, USA"},{"name":"Department of Applied Physical Sciences, University of North Carolina 8 , Chapel Hill, North Carolina 27599, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Scott T.","family":"Grafton","sequence":"additional","affiliation":[{"name":"Department of Psychology and UCSB Brain Imaging Center, University of California 4 , Santa Barbara, California 93106, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2014,1,28]]},"reference":[{"key":"2023062320095099400_c1","volume-title":"Networks: An Introduction","year":"2010"},{"key":"2023062320095099400_c2","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.physrep.2012.03.001","volume":"519","year":"2012","journal-title":"Phys. Rep."},{"key":"2023062320095099400_c3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-36461-7","volume-title":"Temporal Networks","author":"Holme","year":"2013"},{"key":"2023062320095099400_c4","doi-asserted-by":"publisher","first-page":"7641","DOI":"10.1073\/pnas.1018985108","volume":"108","year":"2011","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023062320095099400_c5","doi-asserted-by":"publisher","first-page":"013142","DOI":"10.1063\/1.4790830","volume":"23","year":"2013","journal-title":"Chaos"},{"key":"2023062320095099400_c6","doi-asserted-by":"publisher","first-page":"936","DOI":"10.1016\/j.neuron.2012.03.038","volume":"74","year":"2012","journal-title":"Neuron"},{"key":"2023062320095099400_c7","doi-asserted-by":"publisher","first-page":"033119","DOI":"10.1063\/1.3184538","volume":"19","year":"2009","journal-title":"Chaos"},{"key":"2023062320095099400_c8","doi-asserted-by":"publisher","first-page":"026109","DOI":"10.1103\/PhysRevE.84.026109","volume":"84","year":"2011","journal-title":"Phys. Rev. E"},{"key":"2023062320095099400_c9","unstructured":"A. S.\u2008Waugh, L.\u2008Pei, J. H.\u2008Fowler, P. J.\u2008Mucha, and M. A.\u2008Porter, \u201cParty polarization in Congress: A network science approach,\u201d preprint arXiv:0907.3509 (2012)."},{"key":"2023062320095099400_c10","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1126\/science.1184819","volume":"328","year":"2010","journal-title":"Science"},{"key":"2023062320095099400_c11","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/j.physa.2011.06.030","volume":"391","year":"2012","journal-title":"Physica A"},{"key":"2023062320095099400_c12","first-page":"362","volume-title":"Status, Network, and Structure: Theory Development in Group Processes","year":"1997"},{"key":"2023062320095099400_c13","doi-asserted-by":"publisher","first-page":"115013","DOI":"10.1088\/0266-5611\/27\/11\/115013","volume":"27","year":"2011","journal-title":"Inverse Prob."},{"key":"2023062320095099400_c14","doi-asserted-by":"publisher","first-page":"7332","DOI":"10.1073\/pnas.0610245104","volume":"104","year":"2007","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023062320095099400_c15","doi-asserted-by":"publisher","first-page":"18803","DOI":"10.1073\/pnas.1013140107","volume":"107","year":"2010","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023062320095099400_c16","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1038\/srep00197","volume":"1","year":"2011","journal-title":"Sci. Rep."},{"key":"2023062320095099400_c17","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1056\/NEJMsa066082","volume":"357","year":"2007","journal-title":"New Eng. J. Med."},{"key":"2023062320095099400_c18","first-page":"41","volume-title":"Longitudinal Models in the Behavioral and Related Sciences","author":"Van Montfort","year":"2007"},{"key":"2023062320095099400_c19","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1038\/nphys2342","volume":"8","year":"2012","journal-title":"Nat. Phys."},{"key":"2023062320095099400_c20","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1038\/nphys2327","volume":"8","year":"2012","journal-title":"Nat. Phys."},{"key":"2023062320095099400_c21","volume-title":"Biochemical Lesions and Lethal Synthesis","year":"1963"},{"key":"2023062320095099400_c22","volume-title":"Modern Graph Theory","year":"1998"},{"key":"2023062320095099400_c23","unstructured":"See supplementary material at http:\/\/dx.doi.org\/10.1063\/1.4858457for additional methodological details and supporting results."},{"key":"2023062320095099400_c24","doi-asserted-by":"publisher","first-page":"1459","DOI":"10.4249\/scholarpedia.1459","volume":"2","year":"2007","journal-title":"Scholarpedia"},{"key":"2023062320095099400_c25","volume-title":"Synchronization: A Universal Concept in Nonlinear Sciences","year":"2003"},{"key":"2023062320095099400_c26","volume-title":"Chemical Oscillations, Waves, and Turbulence","year":"1984"},{"key":"2023062320095099400_c27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0167-2789(00)00094-4","volume":"143","year":"2000","journal-title":"Physica D"},{"key":"2023062320095099400_c28","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.physrep.2008.09.002","volume":"469","year":"2008","journal-title":"Phys. Rep."},{"key":"2023062320095099400_c29","doi-asserted-by":"publisher","first-page":"036213","DOI":"10.1103\/PhysRevE.69.036213","volume":"69","year":"2004","journal-title":"Phys. Rev. E"},{"key":"2023062320095099400_c30","doi-asserted-by":"publisher","first-page":"174102","DOI":"10.1103\/PhysRevLett.93.174102","volume":"93","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"2023062320095099400_c31","doi-asserted-by":"publisher","first-page":"114102","DOI":"10.1103\/PhysRevLett.96.114102","volume":"96","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"2023062320095099400_c32","doi-asserted-by":"publisher","first-page":"025109","DOI":"10.1063\/1.3581168","volume":"21","year":"2011","journal-title":"Chaos"},{"key":"2023062320095099400_c33","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1038\/nature03288","volume":"433","year":"2005","journal-title":"Nature"},{"key":"2023062320095099400_c34","doi-asserted-by":"publisher","first-page":"e1003171","DOI":"10.1371\/journal.pcbi.1003171","volume":"9","year":"2013","journal-title":"PLOS Comp. Biol."},{"key":"2023062320095099400_c35","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1002\/hbm.460020107","volume":"2","year":"1994","journal-title":"Hum Brain Mapp"},{"key":"2023062320095099400_c36","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1016\/j.neuron.2011.10.008","volume":"72","year":"2011","journal-title":"Neuron"},{"key":"2023062320095099400_c37","doi-asserted-by":"publisher","first-page":"2196","DOI":"10.1016\/j.neuroimage.2011.10.002","volume":"59","year":"2012","journal-title":"Neuroimage"},{"key":"2023062320095099400_c38","doi-asserted-by":"crossref","unstructured":"M.\u2008Kivel\u00e4, A.\u2008Arenas, M.\u2008Barthelemy, J. P.\u2008Gleeson, Y.\u2008Moreno, and M. A.\u2008Porter, \u201cMultilayer networks,\u201d preprint arXiv:1309.7233 (2013).","DOI":"10.2139\/ssrn.2341334"},{"key":"2023062320095099400_c39","doi-asserted-by":"publisher","first-page":"026111","DOI":"10.1103\/PhysRevE.75.026111","volume":"75","year":"2007","journal-title":"Phys. Rev. E"},{"key":"2023062320095099400_c40","doi-asserted-by":"publisher","first-page":"058702","DOI":"10.1103\/PhysRevLett.111.058702","volume":"111","year":"2013","journal-title":"Phys. Rev. Lett."}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/1.4858457\/13918148\/013112_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/1.4858457\/13918148\/013112_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T10:07:11Z","timestamp":1687601231000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/24\/1\/013112\/135520\/Cross-linked-structure-of-network-evolution"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,28]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,3,1]]}},"URL":"https:\/\/doi.org\/10.1063\/1.4858457","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2014,3]]},"published":{"date-parts":[[2014,1,28]]},"article-number":"013112"}}