Artículo
Topological scale framework for hypergraphs
Autor/es | Molina Abril, Helena
Morón Fernández, María José Benito Marimón, Marc Díaz del Río, Fernando Real Jurado, Pedro |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores |
Fecha de publicación | 2025-01-15 |
Fecha de depósito | 2024-09-06 |
Publicado en |
|
Resumen | In this paper, a new computational topological framework for hypergraph analysis and recognition is developed. “Topology provides scale” is the principle at the core of this set of algebraic topological tools, whose ... In this paper, a new computational topological framework for hypergraph analysis and recognition is developed. “Topology provides scale” is the principle at the core of this set of algebraic topological tools, whose fundamental notion is that of a scale-space topological model (s2-model). The scale of this parameterized sequence of algebraic hypergraphs, all having the same EulerPoincaré characteristic than the original hypergraph G, is provided by its relational topology in terms of evolution of incidence or adjacency connectivity maps. Its algebraic homological counterpart is again an s2-model, allowing the computation of new topological characteristics of G, which far exceeds current homological analytical techniques. Both scale-space algebraic dynamical systems are hypergraph isomorphic invariants. The hypergraph isomorphism problem is attacked here to demonstrate the power of the proposed framework, by proving the ability of s2-models to differentiate challenging cases that are difficult or even infeasible for state-of-the-art practical polynomial solvers. The processing, analysis, classification and learning power of the s2-model, at both combinatorial and algebraic levels, augurs positive prospects with respect to its application to physical, biological and social network analysis. |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) European Union (UE) |
Identificador del proyecto | PID2023-147795NA-I00
PID2023-151065OBI00 TED2021-130825B-I00 MICIU/AEI/10.13039/501100011033 |
Cita | Molina Abril, H., Morón Fernández, M.J., Benito Marimón, M., Díaz del Río, F. y Real Jurado, P. (2025). Topological scale framework for hypergraphs. Applied Mathematics and Computation, 485 (128989). https://doi.org/10.1016/j.amc.2024.128989. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Topological scale framework for ... | 1.690Mb | [PDF] | Ver/ | |