Recency-based preferential attachment models

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. However, they do not allow to model the so-called recency property. Recency property reflects the fact that in many real networks vertices tend to connect to other vertices of similar age. This fact motivated us to introduce and analyse a new class of models-recency-based models. This class is a generalization of fitness models, which were suggested by Bianconi and Barabasi. Bianconi and Barabasi extended preferential attachment models with pages' inherent quality or fitness of vertices. To additionally reflect a recency property, it is reasonable to generalize fitness models by adding a recency factor to the attractiveness function. This means that pages are gaining incoming links according to their attractiveness, which is determined by the incoming degree of the page (current popularity), its inherent quality (some page-specific constant) and age (new pages are gaining new links more rapidly). In this paper, we rigorously analyse the degree distribution in the most realistic recency-based model. Also, we prove that this model does reflect the recency property.