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Research Article
Eigensolution of augmented graph products using shifted inverse iteration method
Article first published online: 18 FEB 2010
DOI: 10.1002/nme.2842
Copyright © 2010 John Wiley & Sons, Ltd.
Issue
International Journal for Numerical Methods in Engineering
Volume 83, Issue 5, pages 558–574, 30 July 2010
Additional Information
How to Cite
Kaveh, A. and Fazli, H. (2010), Eigensolution of augmented graph products using shifted inverse iteration method. Int. J. Numer. Meth. Engng., 83: 558–574. doi: 10.1002/nme.2842
Publication History
- Issue published online: 16 JUL 2010
- Article first published online: 18 FEB 2010
- Manuscript Accepted: 4 DEC 2009
- Manuscript Revised: 29 NOV 2009
- Manuscript Received: 1 JUN 2009
- Abstract
- References
- Cited By
Keywords:
- Laplacian;
- adjacency;
- graphs;
- shifted inverse iteration;
- eigenvalues
Abstract
Two important matrices associated with graphs are adjacency and Laplacian matrices. In this paper efficient methods are presented for eigensolution of graph products augmented by other graphs. For augmentations that do not destroy the symmetry of the graph products, a method is proposed for decomposition of matrices resulting in considerable simplification of their eigensolution. For graphs composed of two non-overlapping graph products joined through a small number of link members, a method based on shifted inverse iteration is proposed which utilizes all eigenvalues and eigenvectors of each individual graph products. Owing to the availability of fast methods for eigensolution of graph products, this method simplifies the eigensolution of a variety of graph models and proves to be very efficient in determining the few smallest eigenpairs of these models with high levels of accuracy. Copyright © 2010 John Wiley & Sons, Ltd.