相关论文: Localization of eigenvector centrality in networks…

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be solved by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix…

While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…

In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that…

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…

This work deals with the issue of assessing the influence of a node in the entire network and in the subnetwork to which it belongs as well, adapting the classical idea of vertex centrality. We provide a general definition of relative…

Networks significantly influence social, economic, and organizational outcomes, with centrality measures serving as crucial tools to capture the importance of individual nodes. This paper introduces Laplacian Eigenvector Centrality (LEC), a…

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool…

Vertices with high betweenness and closeness centrality represent influential entities in a network. An important problem for time varying networks is to know a-priori, using minimal computation, whether the influential vertices of the…

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…

This paper is concerned with distributed detection of central nodes in complex networks using closeness centrality. Closeness centrality plays an essential role in network analysis. Evaluating closeness centrality exactly requires complete…

We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based…

We investigate the issue of eigenfunction localization in random fractal lattices embedded in two dimensional Euclidean space. In the system of our interest, there is no diagonal disorder -- the disorder arises from random connectivity of…

This paper investigates the localization problem of a network in 2-D and 3-D spaces given the positions of anchor nodes in a global frame and inter-node relative measurements in local coordinate frames. It is assumed that the local frames…

Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of…

This paper studies 3-D distributed network localization using mixed types of local relative measurements. Each node holds a local coordinate frame without a common orientation and can only measure one type of information (relative position,…

We describe the phenomenon of localization in the epidemic SIS model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below…

Complex networks with directed, local interactions are ubiquitous in nature, and often occur with probabilistic connections due to both intrinsic stochasticity and disordered environments. Sparse non-Hermitian random matrices arise…

The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…

We consider the canonical ensemble of $N$-vertex Erd\H{o}s-R\'enyi (ER) random topological graphs with quenched vertex degree, and with fugacity $\mu$ for each closed triple of bonds. We claim complete defragmentation of large-$N$ graphs…

The self-attention mechanism prevails in modern machine learning. It has an interesting functionality of adaptively selecting tokens from an input sequence by modulating the degree of attention localization, which many researchers speculate…