Related papers: Eigenvalues of Hypergraph Products and Reciprocal …
Given a digraph D, the complementarity spectrum of the digraph is defined as the set of complementarity eigenvalues of its adjacency matrix. This complementarity spectrum has been shown to be useful in several fields, particularly in…
To some extent, graph evolutionary mechanisms can be explained by its spectra. Here, we are interested in two graph operations, namely, motif (subgraph) doubling and attachment that are biologically relevant. We investigate how these two…
A metrized graph is a compact singular 1-manifold endowed with a metric. A given metrized graph can be modelled by a family of weighted combinatorial graphs. If one chooses a sequence of models from this family such that the vertices become…
The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…
Based on matrix perturbation theory, closed-form analytic expansions are studied for a Laplacian eigenvalue of an undirected, possibly weighted graph, which is close to a unique degree in that graph. An approximation is presented to provide…
We show how the spectrum of a graph Laplacian changes with respect to a certain type of rank-one perturbation. We apply our finding to give new short proofs of the spectral version of Kirchhoff's Matrix Tree Theorem and known derivations…
In this paper, we introduce three operations on hypergraphs by using tensors. We show that these three formulations are equivalent and we commonly call them as the tensor join. We show that any hypergraph can be viewed as a tensor join of…
The purpose of this paper is to explore the asymptotics of the eigenvalue spectrum of the Laplacian on 2 dimensional spaces of constant curvature, giving strong experimental evidence for a conjecture of the second author…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
In this paper, we study dual quaternion and dual complex unit gain graphs and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications…
This paper establishes new eigenvalue bounds for combinatorial Laplacians of simplicial complexes, extending previous results for flag complexes by Lew (2024) and general complexes by Shukla and Yogeshwaran (2020). Using elementary…
We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…
In this paper we improve the spectral convergence rates for graph-based approximations of Laplace-Beltrami operators constructed from random data. We utilize regularity of the continuum eigenfunctions and strong pointwise consistency…
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical…
The Helmholtzian matrix of a graph $G=(V(G),E(G))$ is a graph-theoretic analogue of the vector Laplacian (or Helmholtz operator) [S. Li, L. Lu, J.F. Wang, A graph discretization of vector Laplacian, 379 (2026) 446--460]. Motivated by the…
For unsigned graphs G and H, the characteristic polynomial of different graph matrices for edge corona, subdivision vertex neighbourhood corona and subdivision edge neighbourhood corona has already been studied using the concept of coronal.…
Let $\grad$, $\curl$, and $\dv$ be the graph-theoretic analogues of the gradient, curl, and divergence operators from multivariate calculus. The graph Laplacian $-\dv \grad$ gives rise to the celebrated Laplacian matrix, while the matrix…
We introduce a new operation on a class of graphs with the property that the Laplacian eigenvalues of the input and output graphs are related. Based on this operation, we obtain a family of order (square root of n) noncospectral unicyclic…
From the spectral plot of the (normalized) graph Laplacian, the essential qualitative properties of a network can be simultaneously deduced. Given a class of empirical networks, reconstruction schemes for elucidating the evolutionary…
The spectral theory of higher-order symmetric tensors is an important tool to reveal some important properties of a hypergraph via its adjacency tensor, Laplacian tensor, and signless Laplacian tensor. Owing to the sparsity of these…