Related papers: Eigenvalue Spectra of Modular Networks
Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of $q$ communities, the number of eigenvectors corresponding to the $q$ largest eigenvalues form a "community"…
We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…
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…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
The eigenvalue spectrum of the adjacency matrix of a network is closely related to the behavior of many dynamical processes run over the network. In the field of robotics, this spectrum has important implications in many problems that…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
The spectrum of the normalized complex Laplacian for electrical networks is analyzed. We show that eigenvalues lie in a larger region compared to the case of the real Laplacian. We show the existence of eigenvalues with negative real part…
It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical…
The controllability of networks comprising homogeneous multi-input multi-output linear subsystems with linear couplings among them is examined, from a modal perspective. The eigenvalues of the network model are classified into two groups:…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;,…
Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…
In graph signal processing, the graph adjacency matrix or the graph Laplacian commonly define the shift operator. The spectral decomposition of the shift operator plays an important role in that the eigenvalues represent frequencies and the…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…