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decreasing the spectral radius of a graph by link removals

Decreasing the spectral radius of a graph by link removals
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Van Mieghem Piet; Dragan Stevanovicy; Fernando Kuipers; Cong Li; Ruud van de Bovenkamp; Daijie Liu and Huijuan Wang: Decreasing the spectral radius of a graph by link removals, pp. 1-24. In: Physical Review E, vol. 84, no. 1, July 2011.

Fernando Kuipers
Dajie Liu
Piet van Mieghem

The decrease of the spectral radius, an important characterizer of network dynamics, by remov- ing links is investigated. The minimization of the spectral radius by removing m links is shown to be an NP-complete problem, which suggests to consider 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 (x1)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 in- versely 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.

Robustness and Optimization of Complex Networks

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