Counting cliques in a random graph
Taro Sakurai, Norihide Tokushige

TL;DR
This paper derives an asymptotic formula for the expected number of cliques in Erdős-Rényi random graphs, revealing how clique counts scale with graph size and edge probability.
Contribution
It provides a precise asymptotic expression for the expected number of cliques in G(n,p), advancing understanding of clique distribution in random graphs.
Findings
Expected number of cliques scales as n^{(1/(-2 log p))(log n - 2 log log n + O(1))}
Results improve theoretical understanding of clique counts in Erdős-Rényi graphs
Analytical formula applicable for large n and various p values.
Abstract
We show that the expected number of cliques in the Erd\H{o}s-R\'enyi random graph is .
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Taxonomy
TopicsComplex Network Analysis Techniques · Advanced Graph Theory Research
