Approximating the largest eigenvalue of network adjacency matrices

Juan G. Restrepo, Edward Ott, and Brian R. Hunt

Phys. Rev. E 76, 056119 – Published 29 November 2007

Abstract

The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed networks, and linear stability of equilibria of network coupled systems). In this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations. Numerical experiments on simulated networks are used to test our results.

Received 30 May 2007

DOI:https://doi.org/10.1103/PhysRevE.76.056119

Authors & Affiliations

Juan G. Restrepo^1,*, Edward Ott², and Brian R. Hunt³

¹Center for Interdisciplinary Research in Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA
²Department of Physics, Department of Electrical and Computer Engineering, and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
³Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA

^*juanga@neu.edu

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Issue

Vol. 76, Iss. 5 — November 2007

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics