Related papers: The Laplacian Spectrum of Large Graphs Sampled fro…
Effective resistance, which originates from the field of circuits analysis, is an important graph distance in spectral graph theory. It has found numerous applications in various areas, such as graph data mining, spectral graph…
The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. We find that the class of strongly regular graphs attains the maximum of largest…
Effective resistances are ubiquitous in graph algorithms and network analysis. In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair $s$ and $t$. We consider the classical adjacency…
We investigate spectral properties of Kirchhoff Laplacians on radially symmetric antitrees. This class of metric graphs enjoys a rich group of symmetries, which enables us to obtain a decomposition of the corresponding Laplacian into the…
The average effective resistance of a graph is a relevant performance index in many applications, including distributed estimation and control of network systems. In this paper, we study how the average resistance depends on the graph…
In this work, we use the spectral properties of graphons to study stability and sensitivity to noise of deterministic SIS epidemics over large networks. We consider the presence of additive noise in a linearized SIS model and we derive a…
We present a method for proving upper bounds on the eigenvalues of the graph Laplacian. A main step involves choosing an appropriate "Riemannian" metric to uniformize the geometry of the graph. In many interesting cases, the existence of…
In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…
We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…
It is reported that dynamical systems over digraphs have superior performance in terms of system damping and tolerance to time delays if the underlying graph Laplacian has a purely real spectrum. This paper investigates the topological…
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…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
Measuring robustness is a fundamental task for analyzing the structure of complex networks. Indeed, several approaches to capture the robustness properties of a network have been proposed. In this paper we focus on spectral graph theory…
We consider a family of non-compact manifolds $X_\eps$ (``graph-like manifolds'') approaching a metric graph $X_0$ and establish convergence results of the related natural operators, namely the (Neumann) Laplacian $\laplacian {X_\eps}$ and…
Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of…
Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…
Graphons have traditionally served as limit objects for dense graph sequences, with the cut distance serving as the metric for convergence. However, sparse graph sequences converge to the trivial graphon under the conventional definition of…
This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given $O(\log N)$ pairs of voltage and current…