Generalized Preferential Attachment: Tunable Power-Law Degree Distribution and Clustering Coefficient

We propose a common framework for analysis of a wide class of preferential attachment models, which includes LCD, Buckley–Osthus, Holme–Kim and many others. The class is defined in terms of constraints that are sufficient for the study of the degree distribution and the clustering coefficient. We also consider a particular parameterized model from the class and illustrate the power of our approach as follows. Applying our general results to this model, we show that both the parameter of the power-law degree distribution and the clustering coefficient can be controlled via variation of the model parameters. In particular, the model turns out to be able to reflect realistically these two quantitative characteristics of a real network, thus performing better than previous preferential attachment models. All our theoretical results are illustrated empirically.

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