Liang Li, Liu Hao, Gong Shi-Cai
School of Sciences, Zhejiang University of Science and Technology, Hangzhou 310023, China.
Entropy (Basel). 2025 Aug 29;27(9):915. doi: 10.3390/e27090915.
Citation networks are fundamental for analyzing the mechanisms and patterns of knowledge creation and dissemination. While most studies focus on pairwise attachment between papers, they often overlook compound relational structures, such as co-citation. Combining two key empirical features, superlinear node inflow and the temporal decay of node influence, we propose the Triangular Evolutionary Model of Superlinear Growth and Aging (TEM-SGA). The fitting results demonstrate that the TEM-SGA reproduces key structural properties of real citation networks, including degree distributions, generalized degree distributions, and average clustering coefficients. Further structural analyses reveal that the impact of aging varies with structural scale and depends on the interplay between aging and growth, one manifestation of which is that, as growth accelerates, it increasingly offsets aging-related disruptions. This motivates a degenerate model, the Triangular Evolutionary Model of Superlinear Growth (TEM-SG), which excludes aging. A theoretical analysis shows that its degree and generalized degree distributions follow a power law. By modeling interactions among triadic closure, dynamic expansion, and aging, this study offers insights into citation network evolution and strengthens its theoretical foundation.
引文网络对于分析知识创造和传播的机制及模式至关重要。虽然大多数研究聚焦于论文之间的两两关联，但它们常常忽略复合关系结构，比如共引。结合超线性节点流入和节点影响力的时间衰减这两个关键实证特征，我们提出了超线性增长与老化三角演化模型（TEM-SGA）。拟合结果表明，TEM-SGA再现了真实引文网络的关键结构属性，包括度分布、广义度分布和平均聚类系数。进一步的结构分析表明，老化的影响随结构规模而变化，并且取决于老化与增长之间的相互作用，其一种表现是，随着增长加速，它越来越多地抵消与老化相关的干扰。这促使我们提出一个退化模型，即超线性增长三角演化模型（TEM-SG），该模型排除了老化因素。理论分析表明，其度分布和广义度分布遵循幂律。通过对三元闭包、动态扩展和老化之间的相互作用进行建模，本研究为引文网络演化提供了见解，并强化了其理论基础。
