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Abstract: The largest eigenvalue of the adjacency matrix of a network plays animportant role in several network processes (e.g., synchronization ofoscillators, percolation on directed networks, linear stability of equilibriaof network coupled systems, etc.). In this paper we develop approximations tothe largest eigenvalue of adjacency matrices and discuss the relationshipsbetween these approximations. Numerical experiments on simulated networks areused to test our results.



Author: Juan G. Restrepo, Edward Ott, Brian R. Hunt

Source: https://arxiv.org/







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