Related papers: The subdivision of hypergraphs
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Given an arbitrary hypergraph $\mathcal{H}$, we may glue to $\mathcal{H}$ a family of hypergraphs to get a new hypergraph $\mathcal{H}'$ having $\mathcal{H}$ as an induced subhypergraph. In this paper, we introduce three gluing techniques…
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…
Here, we define a subdivision operation for a hypergraph and compute all the eigenvalues of the subdivision of regular and certain non-regular hypergraphs. In non-regular hypergraphs, we investigate the power of regular graphs, various…
With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…
Building on previous work, this paper extends the modeling of political structures from simplicial complexes to hypergraphs. This allows the analysis of more complex political dynamics where agents who are willing to form coalitions contain…
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
The magnitude homology, introduced by R. Hepworth and S. Willerton, offers a topological invariant that enables the study of graph properties. Hypergraphs, being a generalization of graphs, serve as popular mathematical models for data with…
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of…
Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…
Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…
In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These {\it multiarc graphs} naturally interpolate between arc graphs and flip graphs, both well studied objects in low dimensional geometry and…
Graph theory has provided a very useful tool, called topological indices which are a number obtained from the graph $G$ with the property that every graph $H$ isomorphic to $G$, value of a topological index must be same for both $G$ and…