Spectra of complex networks

Eigenvalue spectra of complex networks

Abstract We examine the eigenvalue spectrum, ρ(μ), of the adjacency matrix of a random scale-free network with an average of p edges per vertex using the replica method. We show how in the dense limit, when p → ∞, one can obtain two relatively simple coupled equations whose solution yields ρ(μ) for an arbitrary complex network. For scale-free graphs, with degree distribution exponent λ, we obta...

The Laplacian Spectra of Graphs and Complex Networks

The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the graph Laplacian for given a degree sequence, the Laplacian coefficients, the algebraic connectivity and the graph doubly stochastic matrix, and the spectra of ra...

Nonnegative realization of complex spectra

Eigenvalue spectra of modular networks.

A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often, such spectral features are theoretically obtained by considering only local node properties, such as degree distributions. Many networks, however, possess large-scale modular ...

Complex Gamma Ray Spectra Analysis

The gamma ray spectrometry laboratory of the University of Bucharest was designed for the analysis of low-level radioactivity samples. High efficiency shielded HPGe detectors are used. Efficiency calibration is achieved by complementing experimental calibration with Monte Carlo computation carried out using GESPECOR, also applied for the evaluation of coincidence summing corrections. Low detect...