The Price-Pareto growth model of networks with community structure

We introduce a new analytical framework for modelling degree sequences in individual communities of real-world networks, e.g., citations to papers in different fields. Our work is inspired by Price's model and its recent generalisation called 3DSI (three dimensions of scientific impact), which assumes that citations are gained partly accidentally, and to some extent preferentially. Our generalisation is motivated by existing research indicating significant differences between how various scientific disciplines grow, namely, minding different growth ratios, average reference list lengths, and preferential citing tendencies. Extending the 3DSI model to heterogeneous networks with a community structure allows us to devise new analytical formulas for, e.g., citation number inequality and preferentiality measures. We show that the distribution of citations in a community tends to a Pareto type II distribution. We also present analytical formulas for estimating its parameters and Gini's index. The new model is validated on real citation networks.