[{"date_updated":"2025-12-30T09:05:32Z","month":"11","date_published":"2025-11-01T00:00:00Z","ec_funded":1,"language":[{"iso":"eng"}],"day":"01","citation":{"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>","short":"M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (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.","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.","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>","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>."},"article_number":"122425","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."}],"year":"2025","publication_status":"published","article_processing_charge":"No","OA_type":"closed access","doi":"10.1016/j.ins.2025.122425","article_type":"original","date_created":"2025-06-30T08:48:48Z","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF"}],"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.","author":[{"last_name":"Mahini","full_name":"Mahini, Mohammad","first_name":"Mohammad"},{"last_name":"Beigy","full_name":"Beigy, Hamid","first_name":"Hamid"},{"last_name":"Qadami","full_name":"Qadami, Salman","first_name":"Salman"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"quality_controlled":"1","publisher":"Elsevier","title":"Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality","issue":"11","external_id":{"isi":["001516170500002"]},"type":"journal_article","publication_identifier":{"issn":["0020-0255"]},"volume":719,"publication":"Information Sciences","_id":"19937","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","corr_author":"1","status":"public","scopus_import":"1","isi":1,"intvolume":"       719","department":[{"_id":"HeEd"}]}]