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Lack of Hyperbolicity in Asymptotic Erd\"os--Renyi Sparse Random Graphs

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arxiv 1009.5700 v2 pith:LN6PS3PF submitted 2010-09-28 math.PR cond-mat.stat-mech

Onuttom Narayan , Iraj Saniee , Gabriel H. Tucci This is my paper · ORCID
classification math.PRcond-mat.stat-mech
keywords componentdeltagiantinftyos--renyirandomsparsealmost
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abstract

In this work we prove that the giant component of the Erd\"os--Renyi random graph $G(n,c/n)$ for c a constant greater than 1 (sparse regime), is not Gromov $\delta$-hyperbolic for any positive $\delta$ with probability tending to one as $n\to\infty$. As a corollary we provide an alternative proof that the giant component of $G(n,c/n)$ when c>1 has zero spectral gap almost surely as $n\to\infty$.

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Cited by 1 Pith paper

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  1. Characterizing Hyperbolicity in Graphs

    math.MG 2026-07 reject novelty 6.0 of 10

    The paper claims an exact formula for the maximal Gromov delta among quadruples of fixed diameter in the hyperbolic plane and uses it to derive a normalized graph hyperbolicity score.

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