Item request has been placed! ×
Item request cannot be made. ×
loading  Processing Request

Topological scale framework for hypergraphs

Item request has been placed! ×
Item request cannot be made. ×
loading   Processing Request
اقرأ أكثر حفظ في قائمتي
  • معلومة اضافية
    • Publisher Information:
      Elsevier 2025-01-15
    • نبذة مختصرة :
      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.
    • الموضوع:
      Hypergraph; Abstract cell complex; Chain complex; Homology; Topological hypergraph analysis; Scale-space model; Hypergraph isomorphism; info:eu-repo/semantics/article
    • Availability:
      Open access content. Open access content
      http://creativecommons.org/licenses/by-nc-nd/4.0
      info:eu-repo/semantics/openAccess
      Attribution-NonCommercial-NoDerivatives 4.0 Internacional
    • Note:
      English
    • Other Numbers:
      SUE oai:idus.us.es:11441/162317
      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.
      0096-3003
      1873-5649
      10.1016/j.amc.2024.128989
      1457285901
    • Contributing Source:
      UNIV DE SEVILLA
      From OAIster®, provided by the OCLC Cooperative.
    • الرقم المعرف:
      edsoai.on1457285901
HoldingsOnline