Related papers: Eigenvalues of Hypergraph Products and Reciprocal …
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…
The relationships between eigenvalues and eigenvectors of a product graph and those of its factor graphs have been known for the standard products, while characterization of Laplacian eigenvalues and eigenvectors of the Kronecker product of…
This paper investigates spectral properties of the deformed Laplacian matrix, which merges the Laplacian and signless Laplacian matrices of a graph through a one-parameter family of matrices. We present general results on the eigenvalues of…
The term interlacing refers to systematic inequalities between the sequences of eigenvalues of two operators defined on objects related by a specific oper- ation. In particular, knowledge of the spectrum of one of the objects then implies…
The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two…
We study both $H$ and $E/Z$-eigenvalues of the adjacency tensor of a uniform multi-hypergraph and give conditions for which the largest positive $H$ or $Z$-eigenvalue corresponds to a strictly positive eigenvector. We also investigate when…
Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…
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…
Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian)…
The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…
In recent years, spectral graph neural networks, characterized by polynomial filters, have garnered increasing attention and have achieved remarkable performance in tasks such as node classification. These models typically assume that…
Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…
The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix, normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian matrix of graphs. In Chapter 1, we present a brief…
In this paper, we introduce the class of cored hypergraphs and power hypergraphs, and investigate the properties of their Laplacian H-eigenvalues. From an ordinary graph, one may generate a $k$-uniform hypergraph, called the $k$th power…
We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a finite number that have limits not on these curves.
The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…