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.

翻译：我们提出了一种新的分析框架，用于建模现实世界网络中单个社区的度序列，例如不同领域论文的引用关系。本研究受到近期对Price模型的改进所启发，该改进假设引用的获得部分出于偶然，部分则遵循优先连接机制。我们的工作旨在解决表征不同科学领域异质性的需求，因为标准的同质模型无法捕捉各领域间差异化的增长比率与引用文化。将该模型扩展至具有社区结构的网络，使我们能够推导出各聚类中引用数量及其基尼系数所描述的不平等性等指标的分析公式。我们还证明每个社区中的引用数量分布倾向于收敛于帕累托II型分布。借助推导出的模型参数估计量，该新模型可适用于实际引用网络及类似网络。