Efficient Maintenance of Leiden Communities in Large Dynamic Graphs

Abstract: As a well-known community detection algorithm, Leiden has been widely used in various scenarios such as LLM generation (e.g., Graph-RAG), anomaly detection, and biological analysis. In these scenarios, the graphs are often large and dynamic, where vertices and edges are inserted and deleted frequently, so it is costly to obtain the updated communities by Leiden from scratch when the graph has changed. Recently, one work has attempted to study how to maintain Leiden communities in the dynamic graph, but it lacks a detailed theoretical analysis, and its algorithms are inefficient for large graphs. To address these issues, in this paper, we first theoretically show that the existing algorithms are relatively unbounded via the boundedness analysis (a powerful tool for analyzing incremental algorithms on dynamic graphs), and also analyze the memberships of vertices in communities when the graph changes. Based on theoretical analysis, we develop a novel efficient maintenance algorithm, called Hierarchical Incremental Tree Leiden (HIT-Leiden), which effectively reduces the range of affected vertices by maintaining the connected components and hierarchical community structures. Comprehensive experiments in various datasets demonstrate the superior performance of HIT-Leiden. In particular, it achieves speedups of up to five orders of magnitude over existing methods.