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The role of persistent graphs in the agreement seeking of social networks
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2013 (English)In: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 31, no 9, 595-606 p.Article in journal (Refereed) Published
Abstract [en]

This paper investigates the role persistent relations play for a social network to reach a global belief agreement under discrete-time or continuous-time evolution. Each directed arc in the underlying communication graph is assumed to be associated with a time-dependent weight function, which describes the strength of the information flow from one node to another. An arc is said to be persistent if its weight function has infinite L1 or l1 norm for continuous or discrete belief evolutions, respectively. The graph that consists of all persistent arcs is called the persistent graph of the underlying network. Three necessary and sufficient conditions on agreement or ε-agreement are established. We prove that the persistent graph fully determines the convergence to a common opinion in a social network. It is shown how the convergence rate explicitly depends on the diameter of the persistent graph. For a social networking service like Facebook, our results indicate how permanent friendships need to be and what network topology they should form for the network to be an efficient platform for opinion diffusion.

Place, publisher, year, edition, pages
2013. Vol. 31, no 9, 595-606 p.
Keyword [en]
Consensus, Dynamical Systems, Non-smooth analysis, Persistent Graphs, Social Networks
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-133399DOI: 10.1109/JSAC.2013.SUP.0513052ISI: 000326262800053Scopus ID: 2-s2.0-84883402176OAI: oai:DiVA.org:kth-133399DiVA: diva2:661584
Note

QC 20131104

Available from: 2013-11-04 Created: 2013-10-31 Last updated: 2017-12-06Bibliographically approved

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Johansson, Karl Henrik

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