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Remarks on power-law random graphs

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  • Yin, Mei

Abstract

The theory of graphons is an important tool in understanding properties of large networks. We investigate a power-law random graph model and cast it in the graphon framework. The distinctively different structures of the limit graph are explored in detail in the sub-critical and super-critical regimes. In the sub-critical regime, the graph is empty with high probability, and in the rare event that it is non-empty, it consists of a single edge. Contrarily, in the super-critical regime, a non-trivial random graph exists in the limit, and it serves as an uncovered boundary case between different types of graph convergence.

Suggested Citation

  • Yin, Mei, 2022. "Remarks on power-law random graphs," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 183-197.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:183-197
    DOI: 10.1016/j.spa.2022.08.002
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    References listed on IDEAS

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    1. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
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