相关论文: Spectral properties of weighted line digraphs
We study the spectral curves of dimer models on periodic Fisher graphs, obtained from a ferromagnetic Ising model on $\mathbb{Z}^2$. The spectral curve is defined by the zero locus of the determinant of a modified weighted adjacency matrix.…
This paper deals with spectral graph theory issues related to questions of monotonicity and comparison of eigenvalues. We consider finite directed graphs with non symmetric edge weights and we introduce a special self-adjoint operator as…
We study isospectrality for mixed Dirichlet-Neumann boundary conditions, and extend the previously derived graph-theoretic formulation of the transplantation method. Led by the theory of Brownian motion, we introduce vertex-colored and…
An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with…
This paper examines the spectral characterizations of oriented graphs. Let $\Sigma$ be an $n$-vertex oriented graph with skew-adjacency matrix $S$. Previous research mainly focused on self-converse oriented graphs, proposing arithmetic…
This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity)…
Spectral characterization of graphs is an important topic in spectral graph theory, which has received a lot of attention from researchers in recent years. It is generally very hard to show a given graph to be determined by its spectrum.…
This paper provides a description of the spectrum of diagonal perturbation of weighted shift operator acting on a separable Hilbert space.
We address the problem of inferring an undirected graph from nodal observations, which are modeled as non-stationary graph signals generated by local diffusion dynamics that depend on the structure of the unknown network. Using the…
In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network's adjacency matrix up to a set of eigenvalues…
We examine transmission through a quantum graph vertex to which auxiliary edges with constant potentials are attached. We find a characterization of vertex couplings for which the transmission probability from a given "input" line to a…
This paper proposes a compression framework for adjacency matrices of weighted graphs based on graph filter banks. Adjacency matrices are widely used mathematical representations of graphs and are used in various applications in signal…
A mixed graph $G$ is a graph obtained from a simple undirected graph by orientating a subset of edges. $G$ is self-converse if it is isomorphic to the graph obtained from $G$ by reversing each directed edge. For two mixed graphs $G$ and $H$…
Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its…
The edge-connectivity matrix of a weighted graph is the matrix whose off-diagonal $v$-$w$ entry is the weight of a minimum edge cut separating vertices $v$ and $w$. Its computation is a classical topic of combinatorial optimization since at…
In graph signal processing, the graph adjacency matrix or the graph Laplacian commonly define the shift operator. The spectral decomposition of the shift operator plays an important role in that the eigenvalues represent frequencies and the…
A $t$-spanner of a weighted undirected graph $G=(V,E)$, is a subgraph $H$ such that $d_H(u,v)\le t\cdot d_G(u,v)$ for all $u,v\in V$. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all…
The scaled relative graph (SRG) of an operator is a subset of the complex plane. It captures several salient features of an operator, such as contractiveness, and can be used to reveal the geometric nature of many of the inequality based…
By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidations, which vertices are the elementary sets…
Here, we suggest a method to represent general directed uniform and non-uniform hypergraphs by different connectivity tensors. We show many results on spectral properties of undirected hypergraphs also hold for general directed uniform…