Related papers: Subdivision method in the Laplacian matching polyn…

Laplace learning is a popular machine learning algorithm for finding missing labels from a small number of labelled feature vectors using the geometry of a graph. More precisely, Laplace learning is based on minimising a graph-Dirichlet…

Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs…

The degree matrix of a graph is the diagonal matrix with diagonal entries equal to the degrees of the vertices of $X$. If $X_1$ and $X_2$ are graphs with respective adjacency matrices $A_1$ and $A_2$ and degree matrices $D_1$ and $D_2$, we…

Protein function prediction is the important problem in modern biology. In this paper, the un-normalized, symmetric normalized, and random walk graph Laplacian based semi-supervised learning methods will be applied to the integrated network…

We study graph-based Laplacian semi-supervised learning at low labeling rates. Laplacian learning uses harmonic extension on a graph to propagate labels. At very low label rates, Laplacian learning becomes degenerate and the solution is…

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…

In this work, we present a theoretical study of signals with sparse representations in the vertex domain of a graph, which is primarily motivated by the discrepancy arising from respectively adopting a synthesis and analysis view of the…

This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Through this method, old and new bounds are derived and numerical examples are provided, showing how former results…

Let $G$ be a graph of order $n$ with degree sequence $d_1 \geq \cdots \geq d_{n}$. Let $m_{G}I$ be the number of signless Laplacian eigenvalues in an interval $I$. In this paper, we characterize the distribution of the signless Laplacian…

This paper has dual aims. First is to develop practical universal coding methods for unlabeled graphs. Second is to use these for graph anomaly detection. The paper develops two coding methods for unlabeled graphs: one based on the degree…

Given a sample from a probability measure with support on a submanifold in Euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold. The graph Laplacian of such a graph is used in…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

A signless Laplacian eigenvalue of a graph $G$ is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, we first give the necessary and sufficient conditions for a…

Let $G$ be a finite non abelian group. The centralizer graph of $G$ is a simple undirected graph $\Gamma_{cent}(G)$, whose vertex set consists of proper centralizers of $G$ and two vertices are adjacent if and only if their cardinalities…

We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…

In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally…

Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In…

The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…

In this paper, we focus on the study of immanantal polynomials for linear combination matrices composed of the degree matrix and adjacency matrix of a graph. First, applying the concept of vertex orientation for general graphs, we provide a…

We introduce the concept of piecewise interlacing zeros for studying the relation of root distribution of two polynomials. The concept is pregnant with an idea of confirming the real-rootedness of polynomials in a sequence. Roughly…