Related papers: Sharp Bounds on Eigenvalues via Spectral Embedding…

We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…

We study the spectral convergence of a symmetrized Graph Laplacian matrix induced by a Gaussian kernel evaluated on pairs of embedded data, sampled from a manifold with boundary, a sub-manifold of $\mathbb{R}^m$. Specifically, we deduce the…

One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where mu_1 and mu_n are respectively the maximum and minimum eigenvalues of the adjacency matrix: chi >= 1 +…

Let G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper bounds for the distance signless Laplacian spectral radius of G are…

Kemeny's constant quantifies the expected time for a random walk to reach a randomly chosen vertex, providing insight into the global behavior of a Markov chain. We present a novel eigenvector-based formula for computing Kemeny's constant.…

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…

We introduce probabilistic embeddings using Laplacian priors (PELP). The proposed model enables incorporating graph side-information into static word embeddings. We theoretically show that the model unifies several previously proposed…

Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…

The abelian sandpile model defines a Markov chain whose states are integer-valued functions on the vertices of a simple connected graph $G$. By viewing this chain as a (nonreversible) random walk on an abelian group, we give a formula for…

We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by Grone, and Grone and…

The properties of a hypergraph explored through the spectrum of its unified matrix was made by the authors in [26]. In this paper, we introduce three different hypergraph matrices: unified Laplacian matrix, unified signless Laplacian…

We study the empirical spectral distribution of the normalized Laplacian of linear preferential attachment graphs in the Barab{\'a}si-Albert regime with fixed out-degree. For the resulting sequence of random multigraphs, we prove that the…

Exact eigendecomposition of large matrices is very expensive, and it is practically impossible to compute exact eigenvalues. Instead, one may set a more modest goal of approaching the empirical distribution of the eigenvalues, recovering…

Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…

Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…

Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we…

Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors…

We give a short and completely elementary method to find the full spectrum of the exclusion process and a nicely limited superset of the spectrum of the interchange process (a.k.a.\ random transpositions) on the complete graph. In the case…

We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a…

The eigenvalues of the normalized Laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects, specifically in relation to random walks. In this paper we determine…