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The Kronecker-clique model for higher-order clustering coefficients

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  • Li, Jin-Yue
  • Li, Xiang
  • Li, Cong

Abstract

We propose a Kronecker-clique model, which possesses the higher-order properties, i.e., high-order clustering coefficients, of real-world networks. The higher-order clustering coefficient is defined as the closure probability of cliques. The higher-order structure of Kronecker-clique model is formed by introducing some cliques into the stochastic Kronecker model according to the degree-dependent function. We compare the higher-order clustering coefficients of the Kronecker-clique model with those of the stochastic Kronecker model and the HyperKron model when fitting the real-world networks. The results indicate that the Kronecker-clique model performs better than the stochastic Kronecker model, the HyperKron model as well as the traditional clustered model. Moreover, we perform k-core decomposition and show that the maximum k-core of the Kronecker-clique model is closer to that of real-world networks compared with the stochastic Kronecker model.

Suggested Citation

  • Li, Jin-Yue & Li, Xiang & Li, Cong, 2021. "The Kronecker-clique model for higher-order clustering coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    • Handle: RePEc:eee:phsmap:v:582:y:2021:i:c:s0378437121005422
    DOI: 10.1016/j.physa.2021.126269
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    1. Gergely Palla & Imre Derényi & Illés Farkas & Tamás Vicsek, 2005. "Uncovering the overlapping community structure of complex networks in nature and society," Nature, Nature, vol. 435(7043), pages 814-818, June.
    2. Cong Li & Qian Li & Piet Mieghem & H. Stanley & Huijuan Wang, 2015. "Correlation between centrality metrics and their application to the opinion model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(3), pages 1-13, March.
    3. Traud, Amanda L. & Mucha, Peter J. & Porter, Mason A., 2012. "Social structure of Facebook networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4165-4180.
    4. Slater, Noa & Itzchack, Royi & Louzoun, Yoram, 2014. "Mid size cliques are more common in real world networks than triangles," Network Science, Cambridge University Press, vol. 2(3), pages 387-402, December.
    5. Martin Rosvall & Alcides V. Esquivel & Andrea Lancichinetti & Jevin D. West & Renaud Lambiotte, 2014. "Memory in network flows and its effects on spreading dynamics and community detection," Nature Communications, Nature, vol. 5(1), pages 1-13, December.
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    1. Wu, Rui-Jie & Kong, Yi-Xiu & Di, Zengru & Zhang, Yi-Cheng & Shi, Gui-Yuan, 2022. "Analytical solution to the k-core pruning process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).

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