相关论文: Extending Graph Burning to Hypergraphs

Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…

For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…

Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the…

Label propagation is a powerful and flexible semi-supervised learning technique on graphs. Neural networks, on the other hand, have proven track records in many supervised learning tasks. In this work, we propose a training framework with a…

The burning number of a graph $G$ is the smallest number $b$ such that the vertices of $G$ can be covered by balls of radii $0, 1, \dots, b-1$. As computing the burning number of a graph is known to be NP-hard, even on trees, it is natural…

Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…

In recent years, large language models (LLMs) have emerged as promising candidates for graph tasks. Many studies leverage natural language to describe graphs and apply LLMs for reasoning, yet most focus narrowly on performance benchmarks…

Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…

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…

Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…

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…

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…

We are developing an interactive graph exploration system called Graph Playground for making sense of large graphs. Graph Playground offers a fast and scalable edge decomposition algorithm, based on iterative vertex-edge peeling, to…

This paper provides a survey of methods, results, and open problems on graph and hypergraph colourings, with a particular emphasis on semi-random `nibble' methods. We also give a detailed sketch of some aspects of the recent proof of the…

Given a graph $G=(V,E)$, the problem of \gb{} is to find a sequence of nodes from $V$, called burning sequence, in order to burn the whole graph. This is a discrete-step process, in each step an unburned vertex is selected as an agent to…

Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…

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…