Related papers: On the Eigenvalues of Graphs with Mixed Algebraic …
In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get…
We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…
A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often such spectral…
We derive the spectral properties of adjacency matrix of complex networks and of their Laplacian by the replica method combined with a dynamical population algorithm. By assuming the order parameter to be a product of Gaussian…
Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…
In this paper, we introduce a matrix for a mixed graph, called the integrated adjacency matrix. This matrix uniquely determines a mixed graph, as long as the indices of the matrix are specified. Additionally, we associate an (undirected)…
The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the…
Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how…
In this article we consider the spectrum of a Laplacian matrix, also known as the Markov matrix, under the independence assumption. We assume that the entries have a variance profile. Motivated by recent works on generalized Wigner matrices…
This paper explores interlacing inequalities in the Laplacian spectrum of signed cycles and investigates interlacing relationship between the spectrum of the net-Laplacian of a signed graph and its subgraph formed by removing a vertex…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from a theoretical framework that we developed based on…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
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 investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
Let $G$ be a simple graph, $A(G)$ its adjacency matrix, and $D(G)$ its diagonal degree matrix. In 2022, \citeauthor{Wang2020} (\cite{Wang2020}) defined the family of matrices $L_\alpha$ as the convex linear combination: \[ L_\alpha(G) =…
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to…
We give inequalities relating the eigenvalues of the adjacency matrix and the Laplacian of a graph, and its minimum and maximum degrees. The results are applied to derive new conditions for quasi-randomness of graphs.