Structural entropy is a metric that measures the amount of information embedded in graph structure data under a strategy of hierarchical abstracting. To measure the structural entropy of a dynamic graph, we need to decode the optimal encoding tree corresponding to the best community partitioning for each snapshot. However, the current methods do not support dynamic encoding tree updating and incremental structural entropy computation. To address this issue, we propose Incre-2dSE, a novel incremental measurement framework that dynamically adjusts the community partitioning and efficiently computes the updated structural entropy for each updated graph. Specifically, Incre-2dSE includes incremental algorithms based on two dynamic adjustment strategies for two-dimensional encoding trees, i.e., the naive adjustment strategy and the node-shifting adjustment strategy, which support theoretical analysis of updated structural entropy and incrementally optimize community partitioning towards a lower structural entropy. We conduct extensive experiments on 3 artificial datasets generated by Hawkes Process and 3 real-world datasets. Experimental results confirm that our incremental algorithms effectively capture the dynamic evolution of the communities, reduce time consumption, and provide great interpretability.

翻译：结构熵是一种度量图结构数据在层次抽象策略下所蕴含信息量的指标。为测量动态图的结构熵，我们需要为每个快照解码出对应最佳社区划分的最优编码树。然而，现有方法不支持动态编码树更新与增量式结构熵计算。为解决这一问题，本文提出Incre-2dSE——一种新颖的增量测量框架，能够动态调整社区划分并高效计算更新后图的修正结构熵。具体而言，Incre-2dSE包含基于两种动态调整策略的二维编码树增量算法：朴素调整策略与节点迁移调整策略。这些算法支持更新后结构熵的理论分析，并能通过增量优化社区划分以降低结构熵。我们在3个由霍克斯过程生成的人工数据集和3个真实数据集上进行了大量实验。实验结果证实，我们的增量算法能有效捕捉社区结构的动态演化，显著降低时间消耗，并提供良好的可解释性。