IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v397y2014icp111-120.html
   My bibliography  Save this article

Consensus formation on a simplicial complex of opinions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113011035
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.12.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. J H Johnson, 1981. "Some Structures and Notation of Q-analysis," Environment and Planning B, , vol. 8(1), pages 73-86, March.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liang, Wei & Shi, Yuming & Huang, Qiuling, 2014. "Modeling the Chinese language as an evolving network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 268-276.
    2. Kaye-Blake, William & Li, Frank Y. & Martin, A. McLeish & McDermott, Alan & Neil, Hayley & Rains, Scott, 2009. "A review of Multi-Agent Simulation Models in Agriculture," 2009 Conference, August 27-28, 2009, Nelson, New Zealand 97165, New Zealand Agricultural and Resource Economics Society.
    3. Lu, Xi & Mo, Hongming & Deng, Yong, 2015. "An evidential opinion dynamics model based on heterogeneous social influential power," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 98-107.
    4. Yan Qiang & Bo Pei & Weili Wu & Juanjuan Zhao & Xiaolong Zhang & Yue Li & Lidong Wu, 2014. "Improvement of path analysis algorithm in social networks based on HBase," Journal of Combinatorial Optimization, Springer, vol. 28(3), pages 588-599, October.
    5. Célestin Coquidé & José Lages & Dima Shepelyansky, 2024. "Opinion Formation in the World Trade Network," Post-Print hal-04461784, HAL.
    6. Xiaolan Qian & Wenchen Han & Junzhong Yang, 2024. "From the DeGroot Model to the DeGroot-Non-Consensus Model: The Jump States and the Frozen Fragment States," Mathematics, MDPI, vol. 12(2), pages 1-13, January.
    7. Stephanie Rend'on de la Torre & Jaan Kalda & Robert Kitt & Juri Engelbrecht, 2016. "On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia," Papers 1602.04352, arXiv.org.
    8. Dimitris Tsintsaris & Milan Tsompanoglou & Evangelos Ioannidis, 2024. "Dynamics of Social Influence and Knowledge in Networks: Sociophysics Models and Applications in Social Trading, Behavioral Finance and Business," Mathematics, MDPI, vol. 12(8), pages 1-27, April.
    9. Gabrielle Demange, 2012. "On the influence of a ranking system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 431-455, July.
    10. Hang-Hyun Jo & Jeoung-Yoo Kim, 2012. "Competitive Targeted Marketing," ISER Discussion Paper 0834, Institute of Social and Economic Research, Osaka University.
    11. Tsao, J.Y. & Boyack, K.W. & Coltrin, M.E. & Turnley, J.G. & Gauster, W.B., 2008. "Galileo's stream: A framework for understanding knowledge production," Research Policy, Elsevier, vol. 37(2), pages 330-352, March.
    12. Pier Paolo Saviotti, 2011. "Knowledge, Complexity and Networks," Chapters, in: Cristiano Antonelli (ed.), Handbook on the Economic Complexity of Technological Change, chapter 6, Edward Elgar Publishing.
    13. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    14. Chung-Yuan Huang & Chuen-Tsai Sun & Hsun-Cheng Lin, 2005. "Influence of Local Information on Social Simulations in Small-World Network Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(4), pages 1-8.
    15. Ricardo Almeida & Agnieszka B. Malinowska & Tatiana Odzijewicz, 2019. "Optimal Leader–Follower Control for the Fractional Opinion Formation Model," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1171-1185, September.
    16. Sun, Bingbin & Yao, Jialing & Xi, Lifeng, 2019. "Eigentime identities of fractal sailboat networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 338-349.
    17. Piotr Przybyła & Katarzyna Sznajd-Weron & Rafał Weron, 2014. "Diffusion Of Innovation Within An Agent-Based Model: Spinsons, Independence And Advertising," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-22.
    18. Yang, Xu-Hua & Lou, Shun-Li & Chen, Guang & Chen, Sheng-Yong & Huang, Wei, 2013. "Scale-free networks via attaching to random neighbors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3531-3536.
    19. Colizza, Vittoria & Flammini, Alessandro & Maritan, Amos & Vespignani, Alessandro, 2005. "Characterization and modeling of protein–protein interaction networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(1), pages 1-27.
    20. Guzmán-Vargas, L. & Hernández-Pérez, R., 2006. "Small-world topology and memory effects on decision time in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(2), pages 326-332.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:397:y:2014:i:c:p:111-120. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.