Majorizations for the Eigenvectors of Graph-Adjacency Matrices: A Tool for Complex Network Design
نویسندگان
چکیده
We develop majorization results that characterize changes in eigenvector components of a graph’s adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterize changes in dominant eigenvector components for single-row 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), majorizations for components of the subdominant and other eigenvectors upon graph modifications are also obtained.
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