Disparity of Clustering Coefficients in the Holme-Kim Network Model – 2017

with R. I. Oliveira (IMPA) and R. Sanchis (UFMG) – Advances in Applied Probability

Abstract

The Holme‒Kim random graph process is a variant of the Barabási‒Álbert scale-free graph that was designed to exhibit clustering. In this paper we show that whether the model does indeed exhibit clustering depends on how we define the clustering coefficient. In fact, we find that the local clustering coefficient typically remains positive whereas global clustering tends to 0 at a slow rate. These and other results are proven via martingale techniques, such as Freedman’s concentration inequality combined with a bootstrapping argument.

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Advances in Applied Probability

Arxiv