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The Holme-Kim random graph processes is a variant of the Barabasi-Albertscale-free graph that was designed to exhibit clustering. In this paper we showthat whether the model does indeed exhibit clustering depends on how we definethe clustering coefficient. In fact, we find that local clustering coefficientremains typically positive whereas global clustering tends to 0 at a slow rate.These and other results are proven via martingale techniques, such asFreedman's concentration inequality combined with a bootstrapping argument.

Disparity of clustering coefficients in the Holme-Kim network model