Component sizes of rank-2 multiplicative random graphs

2024/10/11 by David Clancy, Clancy, David
Computer Science · Mathematics · #05C80 #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2410.09224

openalex publication_date 2024/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that in three different critical regimes, the masses of the connected components of rank-2 multiplicative random graph converge to lengths of excursions of a thinned Lévy process, perhaps with random coefficients. The three critical regimes are those identified by Bollobás, Janson and Riordan (2007), the interacting regime identified by Konarovskyi and Limic (2021), and what we call the nearly bipartite regime which has recently gained interest for its connection to random intersection graphs. Our results are able to extend some of the results by Baslingker et al. (2023) on component sizes of the stochastic blockmodel with two types and those of Federico (2019) and Wang (2023) on the sizes of the connected components of random intersection graphs.

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