The Price-Pareto growth model of networks with community structure
This work provides a more realistic model for citation networks by accounting for heterogeneous growth across scientific fields, addressing a limitation of homogeneous models.
The authors extend the Price-Pareto growth model to networks with community structure, enabling analytical formulae for citation counts and inequality (Gini index) per community, and show that citation distributions in each community follow a Pareto type II distribution.
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 a recent modification of the Price's model, which assumes that citations are gained partly accidentally, and to some extent preferentially. Our work addresses the need to represent the heterogeneity of various scientific domains, as standard homogeneous models fail to capture the distinct growth ratios and citing cultures of different fields. Extending the model to networks with a community structure allows us to devise the analytical formulae for, amongst others, citation counts in each cluster and their inequality as described by the Gini index. We also show that a citation count distribution in each community tends to a Pareto type II distribution. Thanks to the derived model parameter estimators, the new model can be fitted to real citation and similar networks.