Partitioning Sparse Graphs using the Second Eigenvector of their Graph Laplacian

2000/03/06 by David De Wit, De Wit, David
Computer Science · Engineering · Mathematics · #05C70 #Advanced Graph Theory Research #FOS: Mathematics #Graph theory and applications #Numerical Analysis (math.NA) #VLSI and FPGA Design Techniques

paper · pdf · doi:10.48550/arxiv.math/0003036

openalex publication_date 2000/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second eigenvector of a matrix defined solely in terms of the incidence matrix, called the graph Laplacian. For sparse graphs, the eigenvector can be efficiently computed using the Lanczos algorithm. This graph partitioning algorithm is extended to provide a complete hierarchical subdivision of the graph. The method has been implemented and numerical results obtained both for simple test problems and for several grid graphs.

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