Cheeger constants, structural balance, and spectral clustering analysis for signed graphs

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buir.contributor.authorAtay, Fatihcan M.
dc.citation.epage111616-26en_US
dc.citation.issueNumber1en_US
dc.citation.spage111616-1en_US
dc.citation.volumeNumber343en_US
dc.contributor.authorAtay, Fatihcan M.
dc.contributor.authorLiu, S.
dc.date.accessioned2021-02-20T15:06:45Z
dc.date.available2021-02-20T15:06:45Z
dc.date.issued2020-01-01
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe introduce a family of multi-way Cheeger-type constants{hσk,k=1,2,...,n}on asigned graphΓ=(G,σ) such thathσk=0 if and only ifΓhaskbalanced connectedcomponents. These constants are switching invariant and bring together in a unifiedviewpoint a number of important graph-theoretical concepts, including the classicalCheeger constant, those measures of bipartiteness introduced by Desai-Rao, Trevisan,Bauer–Jost, respectively, on unsigned graphs, and the frustration index (originally calledthelineindexofbalancebyHarary)onsignedgraphs.Wefurtherunifythe(higher-orderor improved) Cheeger and dual Cheeger inequalities for unsigned graphs as well as theunderlying algorithmic proof techniques by establishing their corresponding versionson signed graphs. In particular, we develop a spectral clustering method for findingkalmost-balanced subgraphs, each defining a sparse cut. The proper metric for sucha clustering is the metric on a real projective space. We also prove estimates of theextremal eigenvalues of signed Laplace matrix in terms of number of signed triangles(3-cycles).en_US
dc.description.provenanceSubmitted by Evrim Ergin (eergin@bilkent.edu.tr) on 2021-02-20T15:06:45Z No. of bitstreams: 1 Cheeger_constants_structural_balance_and_spectral_clustering_analysis_for_signed_graphs.pdf: 574434 bytes, checksum: 332d9f41bad30d1f28b3d9537dc1d36e (MD5)en
dc.description.provenanceMade available in DSpace on 2021-02-20T15:06:45Z (GMT). No. of bitstreams: 1 Cheeger_constants_structural_balance_and_spectral_clustering_analysis_for_signed_graphs.pdf: 574434 bytes, checksum: 332d9f41bad30d1f28b3d9537dc1d36e (MD5) Previous issue date: 2020-01-01en
dc.embargo.release2022-01-01
dc.identifier.doi10.1016/j.disc.2019.111616en_US
dc.identifier.issn0012-365X
dc.identifier.urihttp://hdl.handle.net/11693/75509
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.disc.2019.111616en_US
dc.source.titleDiscrete Mathematicsen_US
dc.subject05C50en_US
dc.subjectCheeger constanten_US
dc.subjectBipartitenessen_US
dc.subjectStructural balanceen_US
dc.subjectSpectral clusteringen_US
dc.subjectSigned Laplace matrixen_US
dc.titleCheeger constants, structural balance, and spectral clustering analysis for signed graphsen_US
dc.typeArticleen_US

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