Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality

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.

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Journal Article | Epub ahead of print | English

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Author
Mahini, Mohammad; Beigy, Hamid; Qadami, Salman; Saghafian, Morteza

Corresponding author has ISTA affiliation

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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.
Publishing Year
Date Published
2025-06-18
Journal Title
Information Sciences
Publisher
Elsevier
Acknowledgement
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which improved this paper. Work 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.
Volume
719
Issue
11
Article Number
122425
ISSN
IST-REx-ID

Cite this

Mahini M, Beigy H, Qadami S, Saghafian M. Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. Information Sciences. 2025;719(11). doi:10.1016/j.ins.2025.122425
Mahini, M., Beigy, H., Qadami, S., & Saghafian, M. (2025). Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality. Information Sciences. Elsevier. https://doi.org/10.1016/j.ins.2025.122425
Mahini, Mohammad, Hamid Beigy, Salman Qadami, and Morteza Saghafian. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” Information Sciences. Elsevier, 2025. https://doi.org/10.1016/j.ins.2025.122425.
M. Mahini, H. Beigy, S. Qadami, and M. Saghafian, “Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality,” Information Sciences, vol. 719, no. 11. Elsevier, 2025.
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.
Mahini, Mohammad, et al. “Simplet-Based Signatures and Approximation in Simplicial Complexes: Frequency, Degree, and Centrality.” Information Sciences, vol. 719, no. 11, 122425, Elsevier, 2025, doi:10.1016/j.ins.2025.122425.

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