相关论文: Localization of eigenvector centrality in networks…
The detection of the top eigenvalue and its corresponding eigenvector in ensembles of random matrices has significant applications across various fields. An existing method, based on the linear stability of a complementary set of cavity…
We study localization properties of principal eigenvector (PEV) of multilayer networks. Starting with a multilayer network corresponding to a delocalized PEV, we rewire the network edges using an optimization technique such that the PEV of…
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 propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix $A$. The result exploits the Frobenius inner product between $A$ and a given rank-one landmark matrix $X$. Different choices for $X$ may…
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…
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…
It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing…
We describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large. We define the family of functions $f_{\alpha}: \left\{1.2. \dots,…
We report our experiments in identifying large bipartite subgraphs of simple connected graphs which are based on the sign pattern of eigenvectors belonging to the extremal eigenvalues of different graph matrices: adjacency, signless…
We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range to all-to-all coupling. We find a fascinating interplay between interactions and connectivity. In particular, we…
When analyzing the statistical and topological characteristics of complex networks, an effective and convenient way is to compute the centralities for recognizing influential and significant nodes or structures, yet most of them are…
Localization is a fundamental task for sensor networks. Traditional network construction approaches allow to obtain localized networks requiring the nodes to be at least tri-connected (in 2D), i.e., the communication graph needs to be…
In this article we show and implement a simple and effcient method to strictly locate eigenvectors and eigenvalues of a given matrix, based on the modified cone condition. As a consequence we can also effectively localize zeros of complex…
Improving upon results of Rudelson and Vershynin, we establish delocalization bounds for eigenvectors of independent-entry random matrices. In particular, we show that with high probability every eigenvector is delocalized, meaning any…
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…
Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…
Centrality is widely recognized as one of the most critical measures to provide insight in the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework…
This paper poses a question about a simple localization problem. The question is if an {\em oblivious} walker on a line-segment can localize the middle point of the line-segment in {\em finite} steps observing the direction (i.e., Left or…
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…
Numerous centrality measures have been proposed to evaluate the importance of nodes in networks, yet comparative analyses of these measures remain limited. Based on 80 real-world networks, we conducted an empirical analysis of 16…