相关论文: Nodal domains on graphs - How to count them and wh…

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…

A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…

This paper addresses the problem of segmenting a stream of graph signals: we aim to detect changes in the mean of a multivariate signal defined over the nodes of a known graph. We propose an offline method that relies on the concept of…

A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…

In this paper we propose a domain adaptation algorithm designed for graph domains. Given a source graph with many labeled nodes and a target graph with few or no labeled nodes, we aim to estimate the target labels by making use of the…

Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…

We consider the sequence of nodal counts for eigenfunctions of the Laplace-Beltrami operator in two dimensional domains. It was conjectured recently that this sequence stores some information pertaining to the geometry of the domain, and we…

This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…

The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new…

Graph Neural Networks (GNNs) have received a lot of interest in the recent times. From the early spectral architectures that could only operate on undirected graphs per a transductive learning paradigm to the current state of the art…

We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several…

Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is…

Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically…

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…

The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…

When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…

In the paper we discuss how to share the secrets, that are graphs. So, far secret sharing schemes were designed to work with numbers. As the first step, we propose conditions for "graph to number" conversion methods. Hence, the existing…

Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of…

Graphs are widely adopted for modeling complex systems, including financial, biological, and social networks. Nodes in networks usually entail attributes, such as the age or gender of users in a social network. However, real-world networks…