Authors: Van Mieghem, Piet
Stevanović, Dragan 
Kuipers, Fernando
Li, Cong
Van De Bovenkamp, Ruud
Liu, Daijie
Wang, Huijuan
Title: Decreasing the spectral radius of a graph by link removals
Journal: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume: 84
Issue: 1
Issue Date: 6-Jul-2011
Rank: M21a
ISSN: 1539-3755
DOI: 10.1103/PhysRevE.84.016101
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 (x1)i(x 1)j of the components of the eigenvector x1 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.
Publisher: American Physical Society

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