---
res:
  bibo_abstract:
  - Simplets are elementary units within simplicial complexes and are fundamental
    for analyzing the structure of simplicial complexes. Previous efforts have mainly
    focused on accurately counting or approximating the number of simplets rather
    than studying their frequencies. However, analyzing simplet frequencies is more
    practical for large-scale simplicial complexes. This paper introduces the Simplet
    Frequency Distribution (SFD) vector, which enables the analysis of simplet frequencies
    in simplicial complexes. Additionally, we provide a bound on the sample complexity
    required to approximate the SFD vector using any uniform sampling-based algorithm
    accurately. We extend the definition of simplet frequency distribution to encompass
    simplices, allowing for the analysis of simplet frequencies within simplices of
    simplicial complexes. This paper introduces the Simplet Degree Vector (SDV) and
    the Simplet Degree Centrality (SDC), facilitating this analysis for each simplex.
    Furthermore, we present a bound on the sample complexity required for accurately
    approximating the SDV and SDC for a set of simplices using any uniform sampling-based
    algorithm. We also introduce algorithms for approximating SFD, geometric SFD,
    SDV, and SDC. We also validate the theoretical bounds with experiments on random
    simplicial complexes and demonstrate the practical application through a case
    study.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Mohammad
      foaf_name: Mahini, Mohammad
      foaf_surname: Mahini
  - foaf_Person:
      foaf_givenName: Hamid
      foaf_name: Beigy, Hamid
      foaf_surname: Beigy
  - foaf_Person:
      foaf_givenName: Salman
      foaf_name: Qadami, Salman
      foaf_surname: Qadami
  - foaf_Person:
      foaf_givenName: Morteza
      foaf_name: Saghafian, Morteza
      foaf_surname: Saghafian
      foaf_workInfoHomepage: http://www.librecat.org/personId=f86f7148-b140-11ec-9577-95435b8df824
  bibo_doi: 10.1016/j.ins.2025.122425
  bibo_issue: '11'
  bibo_volume: 719
  dct_date: 2025^xs_gYear
  dct_identifier:
  - UT:001516170500002
  dct_isPartOf:
  - http://id.crossref.org/issn/0020-0255
  dct_language: eng
  dct_publisher: Elsevier@
  dct_title: 'Simplet-based signatures and approximation in simplicial complexes:
    Frequency, degree, and centrality@'
...