Evolution of Social Power in Social Networks with Dynamic Topology

The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish sev...

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Main Authors: Ye, Mengbin, Liu, J., Anderson, B.D.O., Yu, C., Başar, T.
Format: Journal Article
Language:English
Published: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC 2018
Subjects:
Online Access:http://purl.org/au-research/grants/arc/DP160104500
http://hdl.handle.net/20.500.11937/84242
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author Ye, Mengbin
Liu, J.
Anderson, B.D.O.
Yu, C.
Başar, T.
author_facet Ye, Mengbin
Liu, J.
Anderson, B.D.O.
Yu, C.
Başar, T.
author_sort Ye, Mengbin
building Curtin Institutional Repository
collection Online Access
description The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individual's social power converges to its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when the network topology is dynamic (i.e., the relative interaction matrix may change between any two successive issues), we show that the initial (perceived) social power of each individual is exponentially forgotten. Specifically, individual social power is dependent only on the dynamic network topology, and initial social power is forgotten as a result of sequential opinion discussion. Finally, we provide an explicit upper bound on an individual's social power as the number of issues discussed tends to infinity; this bound depends only on the network topology. Simulations are provided to illustrate our results.
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institution Curtin University Malaysia
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language English
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publishDate 2018
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spelling curtin-20.500.11937-842422022-10-27T05:05:49Z Evolution of Social Power in Social Networks with Dynamic Topology Ye, Mengbin Liu, J. Anderson, B.D.O. Yu, C. Başar, T. Science & Technology Technology Automation & Control Systems Engineering, Electrical & Electronic Engineering Discrete-time dynamic topology nonlinear contraction analysis opinion dynamics social networks social power LOOKING-GLASS SELF OPINION DYNAMICS CONSENSUS SYSTEMS COORDINATION MATRICES The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individual's social power converges to its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when the network topology is dynamic (i.e., the relative interaction matrix may change between any two successive issues), we show that the initial (perceived) social power of each individual is exponentially forgotten. Specifically, individual social power is dependent only on the dynamic network topology, and initial social power is forgotten as a result of sequential opinion discussion. Finally, we provide an explicit upper bound on an individual's social power as the number of issues discussed tends to infinity; this bound depends only on the network topology. Simulations are provided to illustrate our results. 2018 Journal Article http://hdl.handle.net/20.500.11937/84242 10.1109/TAC.2018.2805261 English http://purl.org/au-research/grants/arc/DP160104500 IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC fulltext
spellingShingle Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Discrete-time
dynamic topology
nonlinear contraction analysis
opinion dynamics
social networks
social power
LOOKING-GLASS SELF
OPINION DYNAMICS
CONSENSUS
SYSTEMS
COORDINATION
MATRICES
Ye, Mengbin
Liu, J.
Anderson, B.D.O.
Yu, C.
Başar, T.
Evolution of Social Power in Social Networks with Dynamic Topology
title Evolution of Social Power in Social Networks with Dynamic Topology
title_full Evolution of Social Power in Social Networks with Dynamic Topology
title_fullStr Evolution of Social Power in Social Networks with Dynamic Topology
title_full_unstemmed Evolution of Social Power in Social Networks with Dynamic Topology
title_short Evolution of Social Power in Social Networks with Dynamic Topology
title_sort evolution of social power in social networks with dynamic topology
topic Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Discrete-time
dynamic topology
nonlinear contraction analysis
opinion dynamics
social networks
social power
LOOKING-GLASS SELF
OPINION DYNAMICS
CONSENSUS
SYSTEMS
COORDINATION
MATRICES
url http://purl.org/au-research/grants/arc/DP160104500
http://hdl.handle.net/20.500.11937/84242