Partitioning Sparse Graphs using the Second Eigenvector of their Graph Laplacian

Details Partitioning Sparse Graphs using the Second Eigenvector of their Graph Laplacian Partitioning Sparse Graphs using the Second Eigenvector of their Graph Laplacian

2000-03-06

arxiv.org/abs/math/0003036v1

Mathematics

Numerical Analysis

Unpublished PGDipSc thesis in the Department of Mathematics at The University of Queensland, Australia. Thesis submitted June

Scientific paper

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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