Related papers: Spectrum of complex networks
The largest eigenvalue of a network's adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
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…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenvectors of matrices associated with graphs to study them. In this paper, we present a collection of $20$ topics in spectral graph theory,…
We undertake an extensive numerical investigation of the graph spectra of thousands regular graphs, a set of random Erd\"os-R\'enyi graphs, the two most popular types of complex networks and an evolving genetic network by using novel…
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…