Incremental Measurement of Structural Entropy for Dynamic Graphs

TL;DR

This paper introduces Incre-2dSE, an incremental framework for efficiently measuring and updating the structural entropy of dynamic graphs, supporting dynamic community detection and reducing computational costs.

Contribution

The paper proposes a novel incremental measurement framework with algorithms for dynamic adjustment of encoding trees, enabling efficient structural entropy computation in evolving graphs.

Findings

Effectively captures community evolution in dynamic graphs

Reduces computation time compared to static methods

Provides interpretable insights into graph structure changes

Abstract

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.