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Framework based on communicability and flow to analyze complex network dynamics

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dc.contributor.author Gilson, Matthieu
dc.contributor.author Kouvaris, Nikos
dc.contributor.author Deco, Gustavo
dc.contributor.author Zamora-López, Gorka
dc.date.accessioned 2021-06-08T09:48:07Z
dc.date.available 2021-06-08T09:48:07Z
dc.date.issued 2018
dc.identifier.citation Gilson M, Kouvaris NE, Deco G, Zamora-López G. Framework based on communicability and flow to analyze complex network dynamics. Phys Rev E. 2018; 97(5):052301. DOI: 10.1103/PhysRevE.97.052301
dc.identifier.issn 2470-0045
dc.identifier.uri http://hdl.handle.net/10230/47795
dc.description.abstract Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagationlike processes such as random walks. However, networks are often inferred from real-data-forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to the mutual relationship between the structure and dynamics in complex networks, as the two sides of the same coin. Here we propose a rigorous framework based on the network response over time (i.e., Green function) to study interactions between nodes across time. For this purpose we define the flow that describes the interplay between the network connectivity and external inputs. This multivariate measure relates to the concepts of graph communicability and the map equation. We illustrate our theory using the multivariate Ornstein-Uhlenbeck process, which describes stable and non-conservative dynamics, but the formalism can be adapted to other local dynamics for which the Green function is known. We provide applications to classical network examples, such as small-world ring and hierarchical networks. Our theory defines a comprehensive framework that is canonically related to directed and weighted networks, thus paving a way to revise the standards for network analysis, from the pairwise interactions between nodes to the global properties of networks including community detection.
dc.description.sponsorship M.G. acknowledges funding from the Marie SkłodowskaCurie Action (Grant No. H2020-MSCA-656547) of the European Commission. G.Z.L., N.E.K., and G.D. acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 720270 (HBP SGA1). G.D. also acknowledges funding from the European Research Council Advanced Grant DYSTRUCTURE (No. 295129) and the Spanish Research Project (No. PSI2013-42091-P). N.E.K. acknowledges support by the “MOVE-IN Louvain” fellowship cofunded by the Marie Skłodowska-Curie Action of the European Commission.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher American Physical Society
dc.relation.ispartof Physical Review E. 2018; 97(5):052301
dc.rights © American Physical Society. Published article available at https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.052301
dc.title Framework based on communicability and flow to analyze complex network dynamics
dc.type info:eu-repo/semantics/article
dc.identifier.doi http://dx.doi.org/10.1103/PhysRevE.97.052301
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/656547
dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/PSI2013-42091
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/720270
dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/295129
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/acceptedVersion

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