Spectral line

Quantum mechanics

Algorithm

Astrophysics

Degenerate energy levels

Eigenvalues and eigenvectors

Computer science

Acoustics

Complex network

Statistical physics

Lattice (music)

Spectrum (functional analysis)

Physics

Mathematics

Adjacency matrix

Spectral properties

Adjacency list

Combinatorics

Chaos An Interdisciplinary Journal of Nonlinear Science

This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part of the spectrum, and (c) degenerate eigenvalues, based on the intrinsic properties of eigenvalues and the phenomena they capture. We have reviewed the works done for spectra of various popular model networks, such as the Erdős-Rényi random networks, scale-free networks, 1-d lattice, small-world networks, and various different real-world networks. Additionally, potential applications of spectral properties for natural processes have been reviewed.

Spectral properties of complex networks