Remarks on power-law random graphs

Mei Yin

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 183-197

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.

Keywords: Power-law random graph; Graph limit; Sub-critical and super-critical regimes (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.08.002

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