Isomorphisms in Multilayer Networks

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorKivela, Mikko
dc.contributor.authorPorter, Mason A.
dc.contributor.departmentDepartment of Computer Science
dc.contributor.departmentUniversity of California Los Angeles
dc.date.accessioned2018-06-18T09:17:52Z
dc.date.available2018-06-18T09:17:52Z
dc.date.issued2017-09-16
dc.description.abstractWe extend the concept of graph isomorphisms to multilayer networks with any number of "aspects" (i.e., types of layering). In developing this generalization, we identify multiple types of isomorphisms. For example, in multilayer networks with a single aspect, permuting vertex labels, layer labels, and both vertex labels and layer labels each yield different isomorphism relations between multilayer networks. Multilayer network isomorphisms lead naturally to defining isomorphisms in any of the numerous types of networks that can be represented as a multilayer network, and we thereby obtain isomorphisms for multiplex networks, temporal networks, networks with both of these features, and more. We reduce each of the multilayer network isomorphism problems to a graph isomorphism problem, where the size of the graph isomorphism problem grows linearly with the size of the multilayer network isomorphism problem. One can thus use software that has been developed to solve graph isomorphism problems as a practical means for solving multilayer network isomorphism problems. Our theory lays a foundation for extending many network analysis methods - including motifs, graphlets, structural roles, and network alignment - to any multilayer network.en
dc.description.versionPeer revieweden
dc.format.mimetypeapplication/pdf
dc.identifier.citationKivela , M & Porter , M A 2017 , ' Isomorphisms in Multilayer Networks ' , IEEE Transactions on Network Science and Engineering . https://doi.org/10.1109/TNSE.2017.2753963en
dc.identifier.doi10.1109/TNSE.2017.2753963
dc.identifier.issn2327-4697
dc.identifier.otherPURE UUID: 09224edd-5997-4b7f-babd-62994a1e9c54
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/09224edd-5997-4b7f-babd-62994a1e9c54
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85030656151&partnerID=8YFLogxK
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/21730033/SCI_Kivela_et_al_Isomorphisms_in_Multilayer.pdf
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/31875
dc.identifier.urnURN:NBN:fi:aalto-201806183293
dc.language.isoenen
dc.relation.ispartofseriesIEEE Transactions on Network Science and Engineeringen
dc.rightsopenAccessen
dc.subject.keywordComplex networks
dc.subject.keywordComputer science
dc.subject.keywordMathematics
dc.subject.keywordMultiplexing
dc.subject.keywordNonhomogeneous media
dc.subject.keywordSoftware
dc.subject.keywordTerminology
dc.subject.keywordTools
dc.titleIsomorphisms in Multilayer Networksen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionacceptedVersion
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