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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. 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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