Hyperbolicity, degeneracy, and expansion of random intersection graphs

2014/09/29 by Matthew Farrell, Timothy D. Goodrich, Farrell, Matthew +9
Computer Science · Mathematics · Physics and Astronomy · #Advanced Graph Theory Research #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Social and Information Networks (cs.SI) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1409.8196

openalex publication_date 2014/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we fully characterize the degeneracy of random intersection graphs, and prove that the model asymptotically almost surely produces graphs with hyperbolicity at least logn. Further, we prove that in the parametric regime where random intersection graphs are degenerate an even stronger notion of sparseness, so called bounded expansion, holds with high probability. We supplement our theoretical findings with experimental evaluations of the relevant statistics.

Citations

• On the Hyperbolicity of Small-World and Tree-Like Random Graphs

Related

• Hyperbolic Random Graphs: Clique Number and Degeneracy with Implications for Colouring
• Random intersection graphs and their applications in security, wireless communication, and social networks
• Random Hyperbolic Graphs: Degree Sequence and Clustering
• Random intersection graphs with communities
• On the Hyperbolicity of Small-World and Tree-Like Random Graphs