Related papers: Coreo-Graph: un progetto di teoria dei grafi e dan…
The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…
In this (mostly) survey article, we give a synopsis of a number of results relating to Brill--Noether theory on curves and metric graphs, together with some speculations about the behavior of one-dimensional linear series on a class of…
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…
Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of…
We propose a new graph-theoretic benchmark in this paper. The benchmark is developed to address shortcomings of an existing widely-used graph benchmark. We thoroughly studied a large number of traditional and contemporary graph algorithms…
Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
Can we learn how to explore unknown spaces efficiently? To answer this question, we study the problem of Online Graph Exploration, the online version of the Traveling Salesperson Problem. We reformulate graph exploration as a reinforcement…
This paper is an attempt to unify coassociative coalgebra theory and random walks on oriented graphs.
In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
For each commutative, graded algebra with finite dimension in each degree, we construct a graded cohomology theory for graphs whose graded Euler characteristic is the chromatic polynomial of the graph. This extends our previous work which…
Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…
Graph learning is a popular approach for performing machine learning on graph-structured data. It has revolutionized the machine learning ability to model graph data to address downstream tasks. Its application is wide due to the…
We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the…
We suggest a measure of "Eulerianness" of a finite directed graph and define a class of "coEulerian" graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application, we address a question in chip-firing posed…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner in 1994 to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which…
A unifying graph theoretic framework for the modelling of metro transportation networks is proposed. This is achieved by first introducing a basic graph framework for the modelling of the London underground system from a diffusion law point…
This study addresses the challenge of forming effective groups in collaborative problem-solving environments. Recognizing the complexity of human interactions and the necessity for efficient collaboration, we propose a novel approach…