Скачать или смотреть 002. Generalized preferential attachment - Людмила Остроумова

Preferential attachment models were shown to be very effective in predicting such important properties of real-world networks as the power-law degree distribution, small diameter, etc. Many different models are based on the idea of preferential attachment. We will speak about a general approach to preferential attachment and define a wide class of models, which includes LCD, Buckley-Osthus, Holme-Kim, random Apollonian network, 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 will also consider a particular parameterized model, which is subject to the general approach and illustrates its capacity as follows. Applying our results to this model, we show that both the exponent 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. We provide an efficient algorithm for generating graphs in this model. All our theoretical results are validated empirically on examples of graphs obtained using this algorithm.