Related papers: Spectral distances on graphs
In this article, we study random graphs with a given degree sequence $d_1, d_2, \cdots, d_n$ from the configuration model. We show that under mild assumptions of the degree sequence, the spectral distribution of the normalized Laplacian…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we…
We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…
The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the…
The spectral dimension $d_s$ of a weighted graph is an exponent associated with the asymptotic behavior of the random walk on the graph. The Ahlfors regular conformal dimension $\dim_\mathrm{ARC}$ of the graph distance is a quasisymmetric…
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…
The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however…
The distance matrix of a graph $G$ is the matrix containing the pairwise distances between vertices. The distance eigenvalues of $G$ are the eigenvalues of its distance matrix and they form the distance spectrum of $G$. We determine the…
The distance matrix of a connected graph is defined as the matrix in which the entries are the pairwise distances between vertices. The distance spectrum of a graph is the set of eigenvalues of its distance matrix. A graph is said to be…
Given any two vertices u, v of a random geometric graph, denote by d_E(u,v) their Euclidean distance and by d_G(u,v) their graph distance. The problem of finding upper bounds on d_G(u,v) in terms of d_E(u,v) has received a lot of attention…
As it is well known, the spectrum $ {\rm sp\,} \Gamma$ (of the adjacency matrix $A$) of a graph $\Gamma$, with $d$ distinct eigenvalues other than its spectral radius $\lambda_0$, usually provides a lot of information about the structure of…
Given $0<\alpha\leq\pi$, ${\epsilon}>0$ and $n$, we define random graphs on the $d$-dimensional sphere by drawing $n$ i.i.d. uniform random points for the vertices, and edges $u {\sim} v$ whenever the geodesic distance between $u$ and $v$…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
We are interested in the general question: to what extent are the spectral properties of a graph connected to the distance function? Our motivation is a concrete example of this question that is due to Steinerberger. We provide some…
From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…
We focus on strongly connected, strong for short, digraphs since in this setting distance is defined for every pair of vertices. Distance ideals generalize the spectrum and Smith normal form of several distance matrices associated with…
The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many…