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How agreement and disagreement evolve over random dynamic 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.
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 6, 1061-1071 p.Article in journal (Refereed) Published
Abstract [en]

The dynamics of an agreement protocol interacting with a disagreement process over a common random network is considered. The model can represent the spreading of true and false information over a communication network, the propagation of faults in a large-scale control system, or the development of trust and mistrust in a society. At each time instance and with a given probability, a pair of network nodes interact. At random each of the nodes then updates its state towards the state of the other node (attraction), away from the other node (repulsion), or sticks to its current state (neglect). Agreement convergence and disagreement divergence results are obtained for various strengths of the updates for both symmetric and asymmetric update rules. Impossibility theorems show that a specific level of attraction is required for almost sure asymptotic agreement and a specific level of repulsion is required for almost sure asymptotic disagreement. A series of sufficient and/or necessary conditions are then established for agreement convergence or disagreement divergence. In particular, under symmetric updates, a critical convergence measure in the attraction and repulsion update strength is found, in the sense that the asymptotic property of the network state evolution transits from agreement convergence to disagreement divergence when this measure goes from negative to positive. The result can be interpreted as a tight bound on how much bad action needs to be injected in a dynamic network in order to consistently steer its overall behavior away from consensus.

Place, publisher, year, edition, pages
2013. Vol. 31, no 6, 1061-1071 p.
Keyword [en]
Consensus algorithms, Dynamic networks, Gossiping, Network science, Opinion dynamics, Social networks, Dynamic network, Communication, Telecommunication networks
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-134451DOI: 10.1109/JSAC.2013.130608ISI: 000319353900008Scopus ID: 2-s2.0-84878129504OAI: oai:DiVA.org:kth-134451DiVA: diva2:676218
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilICT - The Next Generation
Note

QC 20131205

Available from: 2013-12-05 Created: 2013-11-25 Last updated: 2017-12-06Bibliographically approved

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Johansson, Karl Henrik

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