article published yes Mohammad Mahini author Hamid Beigy author Salman Qadami author Morteza Saghafian author f86f7148-b140-11ec-9577-95435b8df824 HeEd department Alpha Shape Theory Extended project Mathematics, Computer Science project Persistence and stability of geometric complexes project 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. Elsevier2025 eng 0020-0255 00151617050000210.1016/j.ins.2025.122425 71911 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>. 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> 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>. 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. 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. M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025). 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> 199372025-06-30T08:48:48Z2025-12-30T09:05:32Z