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 optimal hierarchical community partitioning of the graph. However, the current structural entropy methods do not support efficient incremental updating of encoding trees. 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 snapshot of dynamic graphs. Incre-2dSE consists of an online module and an offline module. The online module includes dynamic measurement 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 supports theoretical analysis of the updated structural entropy and incrementally adjusts the community partitioning towards a lower structural entropy. In contrast, the offline module globally constructs the encoding tree for the updated graph using static community detection methods and calculates the structural entropy by definition. We conduct experiments on an artificial dynamic graph dataset generated by Hawkes Process and 3 real-world datasets. Experimental results confirm that our dynamic measurement algorithms effectively capture the dynamic evolution of the communities, reduce time consumption, and provide great interpretability.

翻译：结构熵是一种度量在层次抽象策略下嵌入图结构数据中信息量的指标。为测量动态图的结构熵，需解码对应图最优层次社区划分的最优编码树。然而，现有结构熵方法不支持编码树的高效增量更新。针对此问题，我们提出Incre-2dSE——一种新颖的增量测量框架，可动态调整社区划分并高效计算动态图每个快照的更新结构熵。Incre-2dSE由在线模块与离线模块组成。在线模块包含基于两种二维编码树动态调整策略（朴素调整策略与节点转移调整策略）的动态测量算法，支持更新结构熵的理论分析，并朝更低结构熵方向增量调整社区划分；离线模块则使用静态社区检测方法全局构建更新图的编码树，并按定义计算结构熵。我们在霍克斯过程生成的人工动态图数据集及3个真实数据集上开展实验。实验结果证实，我们的动态测量算法能有效捕捉社区动态演化、降低时间消耗，并具备良好的可解释性。