Incremental Measurement of Structural Entropy for Dynamic Graphs

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.