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.

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个体社区的度序列，例如不同领域论文的引用情况。我们的研究受到普赖斯模型及其近期推广形式——科学影响力三维模型（3DSI）的启发，该模型假设引用的获得部分具有偶然性，在一定程度上也存在偏好性。我们进行此项推广的动机在于现有研究表明，不同学科领域的增长方式存在显著差异，具体体现在增长比率、平均参考文献列表长度和偏好引用倾向等方面。将3DSI模型推广至具有社区结构的异质网络后，我们得以推导出关于引用数量不平等性和偏好性测度的新解析公式。我们证明社区内的引用分布趋向于帕累托II型分布，并提出了估计其参数及基尼系数的解析公式。新模型在真实引用网络上得到了验证。