{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T04:49:33Z","timestamp":1780375773327,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T00:00:00Z","timestamp":1727827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This work introduces the notion of a hesitant bipolar-valued intuitionistic fuzzy graph (HBVIFG), which reflects four different characterizations: membership with positive\/negative aspects and non-membership with positive\/negative aspects, incorporating multi-dimensional alternatives in all of its information. HBVIFG generalizes both HBVFG and BVHFG due to its diversified nature in observing four perspectives along with multiple attributes in a piece of information. Numerous studies, examples, and graphical representations emphasize the concept\u2019s distinctiveness and importance. The following graph theory terms are defined: strong directed HBVIFG, full directed HBVIFG, directed spanning HBVIFSG, directed HBVIFSG, and partial directed hesitant bipolar-valued intuitionistic fuzzy subgraph (HBVIFSG). Examples of operations utilizing two HBVIFGs are Cartesian, direct, lexicographical, and strong products. A scenario is used to generate the mapping of relations, which includes homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism. We describe a directed HBVIFG application that employs an algorithm to determine the most dominant person and self-persistent person in a social system and a comparative study is also provided. The proposed method provides a more detailed framework for assessing the most dominant and self-persistent individual in a social network across multi-level attributes along with positive and negative side membership and non-membership grades in each element of a network.<\/jats:p>","DOI":"10.3390\/sym16101293","type":"journal-article","created":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T06:27:31Z","timestamp":1727850451000},"page":"1293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hesitant Bipolar-Valued Intuitionistic Fuzzy Graphs for Identifying the Dominant Person in Social Media Groups"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6696-7287","authenticated-orcid":false,"given":"Mohammed","family":"Alqahtani","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, P.O. Box 93499, Riyadh 11673, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Keerthana","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam 613401, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Venkatesh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam 613401, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4709-1857","authenticated-orcid":false,"given":"M.","family":"Kaviyarasu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai 600062, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,2]]},"reference":[{"key":"ref_1","unstructured":"Klir, G.J., and Yuan, B. 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