Majorisations for the eigenvectors of graph-adjacency matrices |
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| Authors: | Rahul Dhal Sandip Roy Yan Wan Ali Saberi |
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| Affiliation: | 1. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, USArdhal@eecs.wsu.edu;3. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, USA;4. Department of Electrical Engineering, University of North Texas, Denton, TX, USA |
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| Abstract: | We develop majorisation results that characterise changes in eigenvector components of a graph's adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterise changes in dominant eigenvector components for single- and multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of the dominant eigenvector. For more limited graph classes (specifically, undirected, and reversibly-structured ones), majorisations for components of the subdominant and other eigenvectors upon graph modifications are also obtained. |
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| Keywords: | algebraic graph theory network design dynamical networks adjacency matrix eigenvectors majorisation |
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