Related papers: Topological Structures of Sets and their Subsets

Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…

Analyzing large complex image collections in domains like forensics, accident investigation, or social media analysis involves interpreting intricate, overlapping relationships among images. Traditional clustering and classification methods…

We generalize the concept of token graphs to obtain supertoken graphs. In the latter case, there can be more than one token in a vertex. We formally define supertoken graphs and establish their basic properties. Moreover, we provide some…

We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…

Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard…

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…

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…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

This paper is the last part of a comprehensive survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…

We study $S(t-1,t,2t)$, which is a special class of Steiner systems. Explicit constructions for designing such systems are developed under a graph-theoretic platform where Steiner systems are represented in the form of uniform hypergraphs.…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…

In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…