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Analytic solution of a static scale-free network model

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  • M. Catanzaro
  • R. Pastor-Satorras

Abstract

We present a detailed analytical study of a paradigmatic scale-free network model, the Static Model. Analytical expressions for its main properties are derived by using the hidden variables formalism. We map the model into a canonic hidden variables one, and solve the latter. The good agreement between our predictions and extensive simulations of the original model suggests that the mapping is exact in the infinite network size limit. One of the most remarkable findings of this study is the presence of relevant disassortative correlations, which are induced by the physical condition of absence of self and multiple connections. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • M. Catanzaro & R. Pastor-Satorras, 2005. "Analytic solution of a static scale-free network model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(2), pages 241-248, March.
    • Handle: RePEc:spr:eurphb:v:44:y:2005:i:2:p:241-248
    DOI: 10.1140/epjb/e2005-00120-9
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
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    1. Pang, Shao-Peng & Hao, Fei, 2018. "Effect of interaction strength on robustness of controlling edge dynamics in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 246-257.
    2. Pang, Shao-Peng & Hao, Fei, 2017. "Controllable subspace of edge dynamics in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 209-223.
    3. Pang, Shaopeng & Hao, Fei, 2017. "Optimizing controllability of edge dynamics in complex networks by perturbing network structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 217-227.
    4. Tamás Sebestyén & Balázs Szabó, 2022. "Market interaction structure and equilibrium price heterogeneity in monopolistic competition," Netnomics, Springer, vol. 22(2), pages 259-282, October.
    5. Pang, Shao-Peng & Hao, Fei, 2018. "Target control of edge dynamics in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 14-26.
    6. Teruyoshi Kobayashi, 2015. "Trend-driven information cascades on random networks," Discussion Papers 1529, Graduate School of Economics, Kobe University.
    7. Liu, Yangyang & Zhao, Chengli & Zhang, Xue & Yi, Dongyun & Chen, Wen, 2018. "Core structure: The coupling failure procedure in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 1-11.

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