Related papers: Localization on low-order eigenvectors of data mat…
We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are…
The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization…
We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex. Three distinct types of…
Information of localization properties of eigenvectors of the complex network has applicability in many different areas which include networks centrality measures, spectral partitioning, development of approximation algorithms, and disease…
The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the…
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…
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
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…
We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
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,…
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 the case of graph partitioning, the emergence of localized eigenvectors can cause the standard spectral method to fail. To overcome this problem, the spectral method using a non-backtracking matrix was proposed. Based on numerical…
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…
Understanding the localization properties of eigenvectors of complex networks is important to get insight into various structural and dynamical properties of the corresponding systems. Here, we analytically develop a scheme to construct a…
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…
Wave localization occurs in all types of vibrating systems, in acoustics, mechanics, optics, or quantum physics. It arises either in systems of irregular geometry (weak localization) or in disordered systems (Anderson localization). We…
We consider $N\times N$ self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with $d$ nonzero entries per row. We show that such random matrices exhibit a canonical localization-delocalization…
Eigenvector centrality is an established measure of global connectivity, from which the importance and influence of nodes can be inferred. We introduce a local eigenvector centrality that incorporates both local and global connectivity.…
The spectrum of the nonbacktracking matrix associated to a network is known to contain fundamental information regarding percolation properties of the network. Indeed, the inverse of its leading eigenvalue is often used as an estimate for…