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...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Language: | English |
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IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
2018
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP160104500 http://hdl.handle.net/20.500.11937/84242 |
| _version_ | 1848764633147506688 |
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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. |
| first_indexed | 2025-11-14T11:22:27Z |
| format | Journal Article |
| id | curtin-20.500.11937-84242 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:22:27Z |
| publishDate | 2018 |
| publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |