Multi-level spectral graph partitioning method

Abstract

In this article, a new method for multi-level and balanced division of non-directional graphs (MSGP) is introduced. Using the eigenvectors of the Laplacian matrix of graphs, the method has a spectral approach which has superiority over local methods (Kernighan–Lin and Fiduccia-Mattheyses) with a global division ability. Bisection, which is a spectral method, can divide the graph by using the Fiedler vector, while the recursive version of this method can divide into multiple levels. However, the spectral methods have two disadvantages: (1) high processing costs; (2) dividing the sub-graphs independently. With a better understanding of the eigenvectors of the whole graph, and by discovering the confidential information owned, MSGP can divide the graphs into balanced and multi-leveled without recursive processing. Inspired by Haar wavelets, it uses the eigenvectors with a binary heap tree. The comparison results in seven existing methods (some are community detection algorithms) on regular and irregular graphs which clearly demonstrate that MSGP works about 14,4 times faster than the others to produce a proper partitioning result.