2007/01/31 by Sarika Jalan, Jayendra N. Bandyopadhyay
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Adjacency matrix #Combinatorics #Complex Network Analysis Techniques #Complex network #Eigenvalues and eigenvectors #Gaussian #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Random matrix #Scale (ratio) #Scale invariance #Statistic #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #physics.bio-ph #q-bio.QM
paper · pdf · doi:10.1103/physreve.76.046107
published as Phys. Rev. E, Vol. 76, 046107 (2007) · accepted in Phys. Rev. E (replaced with the final version)
arxiv created 2007/08/22 · openalex publication_date 2007/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of the adjacency matrix of various model networks, namely, random, scale-free, and small-world networks. These distributions follow the Gaussian orthogonal ensemble statistic of RMT. To probe long-range correlations in the eigenvalues we study spectral rigidity via the Delta3 statistic of RMT as well. It follows RMT prediction of linear behavior in semilogarithmic scale with the slope being approximately 1pi;2 . Random and scale-free networks follow RMT prediction for very large scale. A small-world network follows it for sufficiently large scale, but much less than the random and scale-free networks.