---
OA_type: closed access
_id: '19937'
abstract:
- lang: eng
  text: 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.
acknowledgement: "The authors would like to thank the anonymous reviewers for their
  valuable comments and suggestions, which improved this paper.\r\nWork by the first
  and fourth authors is partially supported by the European Research Council (ERC),
  grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant
  no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science
  Fund (FWF), grant no. I 02979-N35."
article_number: '122425'
article_processing_charge: No
article_type: original
author:
- first_name: Mohammad
  full_name: Mahini, Mohammad
  last_name: Mahini
- first_name: Hamid
  full_name: Beigy, Hamid
  last_name: Beigy
- first_name: Salman
  full_name: Qadami, Salman
  last_name: Qadami
- first_name: Morteza
  full_name: Saghafian, Morteza
  id: f86f7148-b140-11ec-9577-95435b8df824
  last_name: Saghafian
citation:
  ama: 'Mahini M, Beigy H, Qadami S, Saghafian M. Simplet-based signatures and approximation
    in simplicial complexes: Frequency, degree, and centrality. <i>Information Sciences</i>.
    2025;719(11). doi:<a href="https://doi.org/10.1016/j.ins.2025.122425">10.1016/j.ins.2025.122425</a>'
  apa: 'Mahini, M., Beigy, H., Qadami, S., &#38; Saghafian, M. (2025). Simplet-based
    signatures and approximation in simplicial complexes: Frequency, degree, and centrality.
    <i>Information Sciences</i>. Elsevier. <a href="https://doi.org/10.1016/j.ins.2025.122425">https://doi.org/10.1016/j.ins.2025.122425</a>'
  chicago: 'Mahini, Mohammad, Hamid Beigy, Salman Qadami, and Morteza Saghafian. “Simplet-Based
    Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.”
    <i>Information Sciences</i>. Elsevier, 2025. <a href="https://doi.org/10.1016/j.ins.2025.122425">https://doi.org/10.1016/j.ins.2025.122425</a>.'
  ieee: 'M. Mahini, H. Beigy, S. Qadami, and M. Saghafian, “Simplet-based signatures
    and approximation in simplicial complexes: Frequency, degree, and centrality,”
    <i>Information Sciences</i>, vol. 719, no. 11. Elsevier, 2025.'
  ista: 'Mahini M, Beigy H, Qadami S, Saghafian M. 2025. Simplet-based signatures
    and approximation in simplicial complexes: Frequency, degree, and centrality.
    Information Sciences. 719(11), 122425.'
  mla: 'Mahini, Mohammad, et al. “Simplet-Based Signatures and Approximation in Simplicial
    Complexes: Frequency, Degree, and Centrality.” <i>Information Sciences</i>, vol.
    719, no. 11, 122425, Elsevier, 2025, doi:<a href="https://doi.org/10.1016/j.ins.2025.122425">10.1016/j.ins.2025.122425</a>.'
  short: M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).
corr_author: '1'
date_created: 2025-06-30T08:48:48Z
date_published: 2025-11-01T00:00:00Z
date_updated: 2025-12-30T09:05:32Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.ins.2025.122425
ec_funded: 1
external_id:
  isi:
  - '001516170500002'
intvolume: '       719'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa_version: None
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z00342
  name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Information Sciences
publication_identifier:
  issn:
  - 0020-0255
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Simplet-based signatures and approximation in simplicial complexes: Frequency,
  degree, and centrality'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 719
year: '2025'
...