Related papers: Node and layer eigenvector centralities for multip…
In an era where accumulating data is easy and storing it inexpensive, feature selection plays a central role in helping to reduce the high-dimensionality of huge amounts of otherwise meaningless data. In this paper, we propose a graph-based…
A number of recent works have concentrated on a few statistical properties of complex networks, such as the clustering, the right-skewed degree distribution and the community, which are common to many real world networks. In this paper, we…
Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…
The eigenvectors for graph $1$-Laplacian possess some sort of localization property: On one hand, any nodal domain of an eigenvector is again an eigenvector with the same eigenvalue; on the other hand, one can pack up an eigenvector for a…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…
This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…
Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex…
In this paper we introduce a new type of preferential attachment network, the growth of which is based on the eigenvalue centrality. In this network, the agents attach most probably to the nodes with larger eigenvalue centrality which…
Measure the similarity of the nodes in the complex networks have interested many researchers to explore it. In this paper, a new method which is based on the degree centrality and the Relative-entropy is proposed to measure the similarity…
Centrality metrics have been used in various networks, such as communication, social, biological, geographic, or contact networks. In particular, they have been used in order to study and analyze targeted attack behaviors and investigated…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
Complex network theory (CNT) is gaining a lot of attention in the scientific community, due to its capability to model and interpret an impressive number of natural and anthropic phenomena. One of the most active CNT field concerns the…
We present a simple and quick method to approximate network centrality indexes. Our approach, called QuickCent, is inspired by so-called fast and frugal heuristics, which are heuristics initially proposed to model some human decision and…
While a set of covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity. For example, some pairs of variables may be positively correlated across most…
Given a connected graph, the principal eigenvector of the adjacency matrix (often called the Perron vector) can be used to assign positive weights to the vertices. A natural way to measure the homogeneousness of this vector is by…
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…
The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…
This paper systematically studies the behavior of the leading eigenvectors for independent edge undirected random graphs generated from a general latent position model whose link function is possibly infinite rank and also possibly…