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Consensus formation on a simplicial complex of opinions

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  • Maletić, Slobodan
  • Rajković, Milan

Abstract

Geometric realization of an opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically located at the nodes of a scale-free and a random network. Social interactions include all concepts of social dynamics present in the mainstream models, augmented by four additional interaction mechanisms which depend on the local properties of opinions and their overlapping properties. The results pertaining to the formation of consensus are of particular interest. An analogy with quantum mechanical pure states is established through the application of the high-dimensional combinatorial Laplacian.

Suggested Citation

  • Maletić, Slobodan & Rajković, Milan, 2014. "Consensus formation on a simplicial complex of opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 111-120.
    • Handle: RePEc:eee:phsmap:v:397:y:2014:i:c:p:111-120
    DOI: 10.1016/j.physa.2013.12.001
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    References listed on IDEAS

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    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    2. J H Johnson, 1981. "Some Structures and Notation of Q-analysis," Environment and Planning B, , vol. 8(1), pages 73-86, March.
    3. Slobodan Maletić & Danijela Horak & Milan Rajković, 2012. "Cooperation, Conflict And Higher-Order Structures Of Social Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(supp0), pages 1-29.
    4. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1157-1165.
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    Cited by:

    1. Sudhamayee, K. & Krishna, M. Gopal & Manimaran, P., 2023. "Simplicial network analysis on EEG signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    2. Andjelković, Miroslav & Tadić, Bosiljka & Maletić, Slobodan & Rajković, Milan, 2015. "Hierarchical sequencing of online social graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 582-595.
    3. Li Ding & Ping Hu, 2019. "Contagion Processes on Time-Varying Networks with Homophily-Driven Group Interactions," Complexity, Hindawi, vol. 2019, pages 1-13, October.
    4. Hernández Serrano, Daniel & Sánchez Gómez, Darío, 2020. "Centrality measures in simplicial complexes: Applications of topological data analysis to network science," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    5. Hernández Serrano, Daniel & Hernández-Serrano, Juan & Sánchez Gómez, Darío, 2020. "Simplicial degree in complex networks. Applications of topological data analysis to network science," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

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