Related papers: Distinct types of eigenvector localization in netw…
Localization behaviours of Laplacian eigenvectors of complex networks provide understanding to various dynamical phenomena on the corresponding complex systems. We numerically investigate role of hyperedges in driving eigenvector…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
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 consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the…
Using our previously published algorithm, we analyze the eigenvectors of the generalized Laplacian for two metric graphs occurring in practical applications. As expected, localization of an eigenvector is rare and the network should be…
In this article, we consider eigenvector centrality for the nodes of a graph and study the robustness (and stability) of this popular centrality measure. For a given weighted graph {\mathcal G} (both directed and undirected), we consider…
We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…
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"…
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…
Using exact numerical diagonalization, we investigate localization in two classes of random matrices corresponding to random graphs. The first class comprises the adjacency matrices of Erdos-Renyi (ER) random graphs. The second one…
There are different measures to classify a network's data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological…
Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…
Eigenvector centrality is a standard network analysis tool for determining the importance of (or ranking of) entities in a connected system that is represented by a graph. However, many complex systems and datasets have natural multi-way…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
Social networks are discrete systems with a large amount of heterogeneity among nodes (individuals). Measures of centrality aim at a quantification of nodes' importance for structure and function. Here we ask to which extent the most…
Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and…
We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the…
Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards network structures…