Related papers: Laplacian Eigenvector Centrality
In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get…
Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network…
Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic…
Several expressions for the $j$-th component $\left( x_{k}\right)_{j}$ of the $k$-th eigenvector $x_{k}$ of a symmetric matrix $A$ belonging to eigenvalue $\lambda_{k}$ and normalized as $x_{k}^{T}x_{k}=1$ are presented. In particular, the…
The co-occurrence association is widely observed in many empirical data. Mining the information in co-occurrence data is essential for advancing our understanding of systems such as social networks, ecosystem, and brain network. Measuring…
Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to…
We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph…
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…
We study the blind centrality ranking problem, where our goal is to infer the eigenvector centrality ranking of nodes solely from nodal observations, i.e., without information about the topology of the network. We formalize these nodal…
Graph neural networks (GNNs) have achieved remarkable success in a variety of machine learning tasks over graph data. Existing GNNs usually rely on message passing, i.e., computing node representations by gathering information from the…
In this paper, we introduce the Laplacian and the signless Laplacian for the eccentricity matrix of a connected graph, referred to as the eccentricity Laplacian and the eccentricity signless Laplacian, respectively. We establish the…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These…
Though commonly found in the real world, directed networks have received relatively less attention from the literature in which concerns their topological and dynamical characteristics. In this work, we develop a magnetic Laplacian-based…
Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by their popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network…
A metrized graph is a finite weighted graph whose edges are thought of as line segments. In this expository paper, we study the Laplacian operator on a metrized graph and some important functions related to it, including the ``j-function'',…
In this paper we investigate some properties of the Fiedler vector, the so-called first non-trivial eigenvector of the Laplacian matrix of a graph. There are important results about the Fiedler vector to identify spectral cuts in graphs but…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
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…