Related papers: Constructing cospectral hypergraphs
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
This mostly expository paper records some basic facts about towers of homotopy fiber sequences. We give a proof that a pairing of towers induces a pairing of associated spectral sequences, for towers of spaces and towers of spectra.
Predator-prey networks originating from different aqueous and terrestrial environments are compared to assess if the difference in environments of these networks produce any significant difference in the structure of such predator-prey…
In this study, we explore the interrelation between hypergraph symmetries represented by equivalence relations on the vertex set and the spectra of operators associated with the hypergraph. We introduce the idea of equivalence relation…
Spectral tetris is a fexible and elementary method to construct unit norm frames with a given frame operator, having all of its eigenvalues greater than or equal to two. One important application of spectral tetris is the construction of…
Hyperuniform structures possess the ability to confine and drive light, although their fabrication is extremely challenging. Here we demonstrate that speckle patters obtained by a superposition of randomly arranged sources of Bessel beams…
Originating from spectral graph theory, cospectrality is a powerful generalization of exchange symmetry and can be applied to all real-valued symmetric matrices. Two vertices of an undirected graph with real edge weights are cospectral iff…
Copositivity of tensors plays an important role in vacuum stability of a general scalar potential, polynomial optimization, tensor complementarity problem and tensor generalized eigenvalue complementarity problem. In this paper, we propose…
It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we…
This paper studies observability for non-uniform hypergraphs with inputs and outputs. To capture higher-order interactions, we define a canonical non-homogeneous dynamical system with nonlinear outputs on hypergraphs. We then construct…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
A mixed multigraph is obtained from an undirected multigraph by orienting a subset of its edges. In this paper, we study a new Hermitian matrix representation of mixed multigraphs, give an introduction to cospectral operations on mixed…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…
Characterizing graphs by their spectra is a fundamental and challenging problem in spectral graph theory, which has received considerable attention in recent years. A major unsolved conjecture in this area is Haemers' conjecture which…
Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
The spectral radius of a uniform hypergraph $G$ is the the maximum modulus of the eigenvalues of the adjacency tensor of $G$. For $k\ge 2$, among connected $k$-uniform hypergraphs with $m\ge 1$ edges, we show that the $k$-uniform loose path…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…