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Decreasing the spectral radius of a graph by link removals
Piet Van Mieghem1, Dragan Stevanović, Fernando Kuipers
1Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands. P.F.A.VanMieghem@tudelft.nl
Abstract:
The decrease of the spectral radius, an important characterizer of network dynamics, by removing links is investigated. The minimization of the spectral radius by removing m links is shown to be an NP-complete problem, which suggests considering heuristic strategies. Several greedy strategies are compared, and several bounds on the decrease of the spectral radius are derived. The strategy that removes that link l=i~j with largest product (x(1))(i)(x(1))(j) of the components of the eigenvector x(1) belonging to the largest adjacency eigenvalue is shown to be superior to other strategies in most cases. Furthermore, a scaling law where the decrease in spectral radius is inversely proportional to the number of nodes N in the graph is deduced. Another sublinear scaling law of the decrease in spectral radius versus the number m of removed links is conjectured.
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