Expander Hierarchies for Normalized Cuts on Graphs
This work addresses the challenge of making expander decompositions practical for graph clustering, benefiting researchers and practitioners in network analysis, though it is incremental in applying existing theoretical concepts to real-world data.
The paper tackled the problem of computing expander decompositions efficiently in practice and applied it to normalized cut graph clustering, resulting in a solver that outperforms state-of-the-art methods in solution quality by a large margin on various graph types while maintaining competitive running times.
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their inherent intricacies and large hidden factors in their asymptotic running times. Here, we introduce the first practically efficient algorithm for computing expander decompositions and their hierarchies and demonstrate its effectiveness and utility by incorporating it as the core component in a novel solver for the normalized cut graph clustering objective. Our extensive experiments on a variety of large graphs show that our expander-based algorithm outperforms state-of-the-art solvers for normalized cut with respect to solution quality by a large margin on a variety of graph classes such as citation, e-mail, and social networks or web graphs while remaining competitive in running time.