Related papers: Spectral Theory of Hypergraphs: A Survey
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…
Let $H$ be a connected $m$-uniform hypergraph, and let $\mathcal{A}(H)$ be the adjacency tensor of $H$ whose spectrum is simply called the spectrum of $H$. Let $s(H)$ denote the number of eigenvectors of $\mathcal{A}(H)$ associated with the…
This survey is two-fold. We first report new progress on the spectral extremal results on the Tur\'{a}n type problems in graph theory. More precisely, we shall summarize the spectral Tur\'{a}n function in terms of the adjacency spectral…
Here, we represent a general hypergraph by a matrix and study its spectrum. We extend the definition of equitable partition and joining operation for hypergraphs, and use those to compute eigenvalues of different hypergraphs. We derive the…
Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
We give some graph theoretical formulas for the trace $Tr_k(\mathbb {T})$ of a tensor $\mathbb {T}$ which do not involve the differential operators and auxiliary matrix. As applications of these trace formulas in the study of the spectra of…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…
In this paper, we give some bounds for principal eigenvector and spectral radius of connected uniform hypergraphs in terms of vertex degrees, the diameter, and the number of vertices and edges.
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
The spectral analogue of the Tur\'{a}n type problem for hypergraphs is to determine the maximum spectral radius for the hypergraphs of order $n$ that do not contain a given hypergraph. For the hypergraphs among the set of the connected…
In recent years, deep learning techniques revolutionized the way remote sensing data are processed. Classification of hyperspectral data is no exception to the rule, but has intrinsic specificities which make application of deep learning…