Related papers: Topological Simplifications of Hypergraphs
Finding inherent or processed links within a dataset allows to discover potential knowledge. The main contribution of this article is to define a global framework that enables optimal knowledge discovery by visually rendering co-occurences…
Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
The shrinking operation converts a hypergraph into a graph by choosing, from each hyperedge, two endvertices of a corresponding graph edge. A hypertree is a hypergraph which can be shrunk to a tree on the same vertex set. Klimo\v{s}ov\'{a}…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The overlap number of a graph is the minimum number of elements…
The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes -- a purely combinatorial one and two geometric ones. It is shown, that most…
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…
Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize…
Real-world complex networks are usually being modeled as graphs. The concept of graphs assumes that the relations within the network are binary (for instance, between pairs of nodes); however, this is not always true for many real-life…
We define an algebraic setup of homology for hypergraphs, which defaults to simplicial homology in the case of graphs, and study its basic properties. As part of our study we define algebraic spanning trees of hypergraphs, along with…
In this paper we are interested in decomposing a dihypergraph $\mathcal{H} = (V, \mathcal{E})$ into simpler dihypergraphs, that can be handled more efficiently. We study the properties of dihypergraphs that can be hierarchically decomposed…
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…
We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…
Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a…
Euler diagrams are an intuitive and popular method to visualize set-based data. In a Euler diagram, each set is represented as a closed curve, and set intersections are shown by curve overlaps. However, Euler diagrams are not visually…
Connectivity is a central notion of graph theory and plays an important role in graph algorithm design and applications. With emerging new applications in networks, a new type of graph connectivity problem has been getting more…
In recent decades, hypergraphs and their analysis through Topological Data Analysis (TDA) have emerged as powerful tools for understanding complex data structures. Various methods have been developed to construct hypergraphs -- referred to…