Related papers: Eigenvalue Spectra of Modular Networks

The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new…

Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…

Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…

Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…

The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…

The dynamics of networks of interacting systems depends intricately on the interaction topology. When the dynamics is explored, generally the whole topology has to be considered. However, we show that there are certain mesoscale subgraphs…

Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…

The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…

In this article we consider the spectrum of a Laplacian matrix, also known as the Markov matrix, under the independence assumption. We assume that the entries have a variance profile. Motivated by recent works on generalized Wigner matrices…

We study the spectral properties of the process of explosive percolation. In particular, we explore how the maximum eigenvalue of the adjacency matrix of a network which governs the spreading efficiency evolves as the density of connection…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…

Recently developed techniques to acquire high-quality human mobility data allow large-scale simulations of the spread of infectious diseases with high spatial and temporal resolution.Analysis of such data has revealed the oversimplification…

We study identification and inference in nonlinear dynamic systems defined on unknown interaction networks. The system evolves through an unobserved dependence matrix governing cross-sectional shock propagation via a nonlinear operator. We…

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…

We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric null model. This provides for the first time an objective measure of whether or not a particular…

Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or…

Persistent Laplacians are matrix operators that track how the shape and structure of data transform across scales and are popularly adopted in biology, physics, and machine learning. Their eigenvalues are concise descriptors of geometric…

This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced…

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…