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The mathematics of non-linear metrics for nested networks

Author

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  • Wu, Rui-Jie
  • Shi, Gui-Yuan
  • Zhang, Yi-Cheng
  • Mariani, Manuel Sebastian

Abstract

Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness–complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness–complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness–complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.

Suggested Citation

  • Wu, Rui-Jie & Shi, Gui-Yuan & Zhang, Yi-Cheng & Mariani, Manuel Sebastian, 2016. "The mathematics of non-linear metrics for nested networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 254-269.
    • Handle: RePEc:eee:phsmap:v:460:y:2016:i:c:p:254-269
    DOI: 10.1016/j.physa.2016.05.023
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    References listed on IDEAS

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    1. Manuel Sebastian Mariani & Alexandre Vidmer & Matus Medo & Yi-Cheng Zhang, 2015. "Measuring economic complexity of countries and products: which metric to use?," Papers 1509.01482, arXiv.org.
    2. Alexandre Vidmer & An Zeng & Mat'uv{s} Medo & Yi-Cheng Zhang, 2015. "Prediction in complex systems: the case of the international trade network," Papers 1511.05404, arXiv.org.
    3. Manuel Mariani & Alexandre Vidmer & Matsúš Medo & Yi-Cheng Zhang, 2015. "Measuring economic complexity of countries and products: which metric to use?," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(11), pages 1-9, November.
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    8. Vidmer, Alexandre & Zeng, An & Medo, Matúš & Zhang, Yi-Cheng, 2015. "Prediction in complex systems: The case of the international trade network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 188-199.
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    Cited by:

    1. Orazio Angelini & Matthieu Cristelli & Andrea Zaccaria & Luciano Pietronero, 2017. "The complex dynamics of products and its asymptotic properties," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-20, May.
    2. Viktor Stojkoski & Zoran Utkovski & Ljupco Kocarev, 2016. "The Impact of Services on Economic Complexity: Service Sophistication as Route for Economic Growth," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-29, August.
    3. Diogo Ferraz & Fernanda P. S. Falguera & Enzo B. Mariano & Dominik Hartmann, 2021. "Linking Economic Complexity, Diversification, and Industrial Policy with Sustainable Development: A Structured Literature Review," Sustainability, MDPI, vol. 13(3), pages 1-29, January.
    4. Orazio Angelini & Matthieu Cristelli & Andrea Zaccaria & Luciano Pietronero, 2016. "The complex dynamics of products and its asymptotic properties," Papers 1610.00274, arXiv.org, revised May 2017.
    5. Ye, Yucheng & Xu, Shuqi & Mariani, Manuel Sebastian & Lü, Linyuan, 2022. "Forecasting countries' gross domestic product from patent data," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Pintar, Nico & Scherngell, Thomas, 2022. "The complex nature of regional knowledge production: Evidence on European regions," Research Policy, Elsevier, vol. 51(8).
    7. Carlo Piccardi & Lucia Tajoli, 2018. "Complexity, centralization, and fragility in economic networks," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-13, November.
    8. Orazio Angelini & Tiziana Di Matteo, 2018. "Complexity of products: the effect of data regularisation," Papers 1808.08249, arXiv.org, revised Oct 2018.

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