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Weighted assortative and disassortative networks model

Author

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  • Leung, C.C.
  • Chau, H.F.

Abstract

Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by topological growth as well as by weight change. In addition, we introduce the weighted assortativity coefficient, which generalizes the assortativity coefficient of a topological network, to measure the tendency of having a high-weighted link between two vertices of similar degrees. Network generated by our model exhibits scale-free behavior with a tunable exponent. Besides, a few non-trivial features found in real-world networks are reproduced by varying the parameter ruling the speed of weight evolution. Most importantly, by studying the weighted assortativity coefficient, we found that both topologically assortative and disassortative networks generated by our model are in fact weighted assortative.

Suggested Citation

  • Leung, C.C. & Chau, H.F., 2007. "Weighted assortative and disassortative networks model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 591-602.
    • Handle: RePEc:eee:phsmap:v:378:y:2007:i:2:p:591-602
    DOI: 10.1016/j.physa.2006.12.022
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    Citations

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    Cited by:

    1. Sabek, M. & Pigorsch, U., 2023. "Local assortativity in weighted and directed complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    2. Ricca, Federica & Scozzari, Andrea, 2024. "Portfolio optimization through a network approach: Network assortative mixing and portfolio diversification," European Journal of Operational Research, Elsevier, vol. 312(2), pages 700-717.
    3. Stefano Martinazzi & Andrea Flori, 2020. "The evolving topology of the Lightning Network: Centralization, efficiency, robustness, synchronization, and anonymity," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-18, January.
    4. Berndsen, R.J. & Renneboog, L.D.R. & León, C., 2014. "Financial Stability and Interacting Networks of Financial Institutions and Market Infrastructures," Discussion Paper 2014-057, Tilburg University, Center for Economic Research.
    5. Arcagni, Alberto & Cerqueti, Roy & Grassi, Rosanna, 2024. "Higher-order assortativity for directed weighted networks and Markov chains," European Journal of Operational Research, Elsevier, vol. 316(1), pages 215-227.
    6. Kulkarni, Saumitra & Pharasi, Hirdesh K. & Vijayaraghavan, Sudharsan & Kumar, Sunil & Chakraborti, Anirban & Samal, Areejit, 2024. "Investigation of Indian stock markets using topological data analysis and geometry-inspired network measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    7. Pigorsch, U. & Sabek, M., 2022. "Assortative mixing in weighted directed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    8. Arcagni, Alberto & Grassi, Rosanna & Stefani, Silvana & Torriero, Anna, 2021. "Extending assortativity: An application to weighted social networks," Journal of Business Research, Elsevier, vol. 129(C), pages 774-783.
    9. León, Carlos & Berndsen, Ron J., 2014. "Rethinking financial stability: Challenges arising from financial networks’ modular scale-free architecture," Journal of Financial Stability, Elsevier, vol. 15(C), pages 241-256.
    10. León, C., 2015. "Financial stability from a network perspective," Other publications TiSEM bb2e4e44-e842-45c6-a946-4, Tilburg University, School of Economics and Management.
    11. Tabak, Benjamin M. & Serra, Thiago R. & Cajueiro, Daniel O., 2009. "The expectation hypothesis of interest rates and network theory: The case of Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1137-1149.
    12. Olufolajimi Oke & Kavi Bhalla & David C. Love & Sauleh Siddiqui, 2018. "Spatial associations in global household bicycle ownership," Annals of Operations Research, Springer, vol. 263(1), pages 529-549, April.
    13. Hongqi Li & Haotian Wang & Ming Bai & Bin Duan, 2018. "The Structure and Periodicity of the Chinese Air Passenger Network," Sustainability, MDPI, vol. 11(1), pages 1-16, December.
    14. Kephart, Curtis & Friedman, Daniel & Baumer, Matt, 2015. "Emergence of networks and market institutions in a large virtual economy," Discussion Papers, Research Professorship Market Design: Theory and Pragmatics SP II 2015-502, WZB Berlin Social Science Center.

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