2020/08/13 by Mei Yin, Yin, Mei
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2008.05625
openalex publication_date 2020/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.