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 , a novel incremental measurement framework that dynamically adjusts the community partitioning and efficiently computes the updated structural entropy for each updated graph. Specifically, includes incremental algorithms based on two dynamic adjustment strategies for two-dimensional encoding trees, i.e., and , 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 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.

中文翻译：

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动态图结构熵的增量测量


结构熵是一种度量层次抽象策略下嵌入图结构数据中的信息量的指标。为了测量动态图的结构熵，我们需要解码与每个快照的最佳社区划分相对应的最佳编码树。然而，当前的方法不支持动态编码树更新和增量结构熵计算。为了解决这个问题，我们提出了一种新颖的增量测量框架，该框架可以动态调整社区划分并有效计算每个更新图的更新结构熵。具体来说，包括基于二维编码树的两种动态调整策略的增量算法，即 和 ，支持更新结构熵的理论分析，并逐步优化社区划分以获得较低的结构熵。我们对由 3 个人工数据集生成的数据集和 3 个真实世界数据集进行了广泛的实验。实验结果证实，我们的增量算法有效地捕获了社区的动态演化，减少了时间消耗，并提供了良好的可解释性。