Related papers: Hypergraphs: an introduction and review
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
We study several extensions of the notion of perfect graphs to $k$-uniform hypergraphs.
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for an edge of size $t$ to belong to the hypergraph depends of a…
Higher-order network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas…
Generalized connectivity introduced by Hager (1985) has been studied extensively in undirected graphs and become an established area in undirected graph theory. For connectivity problems, directed graphs can be considered as generalizations…
This text is based on a translation of a chapter in a handbook about network analysis (published in German) where we tried to make beginners familiar with some basic notions and recent developments of network analysis applied to…
In the last decade, subgraph detection and enumeration have emerged as a central problem in distributed graph algorithms. This is largely due to the theoretical challenges and practical applications of these problems. In this paper, we…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
The transmission of a connected hypergraph is defined as the summation of distances between all unordered pairs of distinct vertices. We determine the unique uniform unicyclic hypergraphs of fixed size with minimum and maximum…
We present HoloGraphs, a novel approach for physically representing, explaining, exploring, and interacting with dynamic networks. HoloGraphs addresses the challenges of visualizing and understanding evolving network structures by providing…
In 1974, Erd\H{o}s asked the following question: given a graph $G$ and a directed graph $\vec{H}$, how many ways are there to orient the edges of $G$ such that it does not contain $\vec{H}$ as a subgraph? We denote this value by $D(G,…
Almost forty years ago, Connes, Feldman and Weiss proved that for measurable equivalence relations the notions of amenability and hyperfiniteness coincide. In this paper we define the uniform version of amenability and hyperfiniteness for…
Many problems such as node classification and link prediction in network data can be solved using graph embeddings. However, it is difficult to use graphs to capture non-binary relations such as communities of nodes. These kinds of complex…
A hypergraph is a data structure composed of nodes and hyperedges, where each hyperedge is an any-sized subset of nodes. Due to the flexibility in hyperedge size, hypergraphs represent group interactions (e.g., co-authorship by more than…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…
Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…
In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is…
Supertagging is an approach originally developed by Bangalore and Joshi (1999) to improve the parsing efficiency. In the beginning, the scholars used small training datasets and somewhat na\"ive smoothing techniques to learn the probability…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…