A Hierarchical Hypergraph and Superhypergraph Framework for Semantic and Behavioral Graphs in Psychology and the Social Sciences

Authors

https://doi.org/10.48314/nex.vi.27

Abstract

Graph theory—modeling entities as vertices and their relationships as edges—has been applied across
domains from anatomical networks (e.g. teeth) to social systems. In psychology and the social
sciences, Behavior Graphs capture temporal sequences of actions or states, while Semantic Graphs
represent conceptual associations underlying memory and cognition. Here, we extend both models using
HyperGraphs and SuperHyperGraphs to create hierarchical, multi-scale representations. This framework
enables nested modeling of cognitive and behavioral structures, offering a versatile approach for analyzing
complex phenomena in psychological and social research

Keywords:

Superhypergraph, Hypergraph, Semantic Graph, Behavior Graph

References

  1. [1] Diestel, R. (2025). Graph theory (Vol. 173). Springer Nature. https://doi.org/10.1007/978-3-662-70107-2
  2. [2] Gross, J. L., Yellen, J., & Anderson, M. (2018). Graph theory and its applications. Chapman and Hall/CRC. https://www.amazon.nl/-/en/Jonathan-L-Gross/dp/1482249480
  3. [3] Berge, C. (1984). Hypergraphs: Combinatorics of finite sets (Vol. 45). Elsevier. https://B2n.ir/xj7792
  4. [4] Bretto, A. (2013). Hypergraph theory. An introduction: Mathematical engineering (pp. 209-216). Cham: Springer. https://doi.org /10.1007/978-3-319-00080-0
  5. [5] Feng, Y., You, H., Zhang, Z., Ji, R., & Gao, Y. (2019). Hypergraph neural networks. Proceedings of the AAAI conference on artificial intelligence (pp. 3558-3565). Association for the advancement of artificial intelligence (AAAI). https://doi.org/10.1609/aaai.v33i01.33013558
  6. [6] Cai, D., Song, M., Sun, C., Zhang, B., Hong, S., & Li, H. (2022). Hypergraph structure learning for hypergraph neural networks. Proceedings of the thirty-first international joint conference on artificial intelligence (IJCAI-22) (pp. 1923-1929). International joint conferences on artificial intelligence. https://doi.org/10.24963/ijcai.2022/267
  7. [7] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., & Zou, C. (2020). Hypergraph learning: Methods and practices. IEEE transactions on pattern analysis and machine intelligence, 44(5), 2548-2566. https://doi.org/10.1109/TPAMI.2020.3039374
  8. [8] Eiter, T., & Gottlob, G. (2002). Hypergraph transversal computation and related problems in logic and AI. European workshop on logics in artificial intelligence (pp. 549-564). Springer Berlin Heidelberg. https://link.springer.com/chapter/10.1007/3-540-45757-7_53
  9. [9] Stavropoulos, E. C., Verykios, V. S., & Kagklis, V. (2016). A transversal hypergraph approach for the frequent itemset hiding problem. Knowledge and information systems, 47(3), 625-645. https://doi.org/10.1007/s10115-015-0862-3
  10. [10] Wang, Y., Gan, Q., Qiu, X., Huang, X., & Wipf, D. (2023). From hypergraph energy functions to hypergraph neural networks. International conference on machine learning (pp. 35605-35623). Proceedings of machine learning research. https://proceedings.mlr.press/v202/wang23d.html
  11. [11] Hamidi, M., Smarandache, F., & Taghinezhad, M. (2023). Decision making based on valued fuzzy superhypergraphs. Infinite Study. https://B2n.ir/rm7022
  12. [12] Alqahtani, M. (2025). Intuitionistic fuzzy quasi-supergraph integration for social network decision making. International journal of analysis and applications, 23, 137-137. https://doi.org/10.28924/2291-8639-23-2025-137
  13. [13] Nalawade, N. B., Bapat, M. S., Jakkewad, S. G., Dhanorkar, G. A., & Bhosale, D. J. (2025). Structural properties of zero-divisor hypergraph and superhypergraph over Zn: Girth and helly property. Panamerican Mathematical Journal, 35(4S), 485.
  14. [14] Smarandache, F. (2020). Extension of hypergraph to n-superhypergraph and to plithogenic n-superhypergraph, and extension of hyperalgebra to n-ary (Classical-/Neutro-/Anti-) HyperAlgebra. Infinite Study. https://B2n.ir/wj6560
  15. [15] Jácome Mogro, E., Rojas Molina, J., Sandoval Cañas, G. J., & Herrera Soria, P. (2024). Tree tobacco extract (Nicotiana glauca) as a plithogenic bioinsecticide alternative for controlling fruit fly (Drosophila immigrans) using n-superhypergraphs. Neutrosophic Sets and Systems, 74(1), 57-65. https://digitalrepository.unm.edu/nss_journal/vol74/iss1/7/
  16. [16] Diestel, R. (2025). Graph theory (Vol. 173). Springer Nature. https://B2n.ir/re1315
  17. [17] Ugander, J., Karrer, B., Backstrom, L., & Marlow, C. (2011). The anatomy of the facebook social graph. https://doi.org/10.48550/arXiv.1111.4503
  18. [18] Jech, T. (2003). Set theory. The third millennium edition, revised and expanded. Springer-Verlag, Berlin. https://doi.org/10.1017/S1079898600003358
  19. [19] Fried, E. I., Epskamp, S., Nesse, R. M., Tuerlinckx, F., & Borsboom, D. (2016). What are'good'depression symptoms? Comparing the centrality of DSM and non-DSM symptoms of depression in a network analysis. Journal of affective disorders, 189, 314-320. https://doi.org/10.1016/j.jad.2015.09.005
  20. [20] Cramer, A. O., Van Borkulo, C. D., Giltay, E. J., Van Der Maas, H. L., Kendler, K. S., Scheffer, M., & Borsboom, D. (2016). Major depression as a complex dynamic system. PloS one, 11(12), e0167490. https://doi.org/10.1371/journal.pone.0167490
  21. [21] Das, A. K., Das, R., Das, S., Debnath, B. K., Granados, C., Shil, B., & Das, R. (2025). A comprehensive study of neutrosophic superhyper bci-semigroups and their algebraic significance. Transactions on Fuzzy Sets and Systems, 8(2), 80-101. https://doi.org/10.71602/tfss.2025.1198050
  22. [22] Smarandache, F. (2024). Foundation of superhyperstructure & neutrosophic superhyperstructure. Neutrosophic sets and systems, 63(2024), 367-381. https://digitalrepository.unm.edu/nss_journal/vol63/iss1/21/
  23. [23] Smarandache, F. (2024). Superhyperstructure & neutrosophic superhyperstructure. https://digitalrepository.unm.edu/nss_journal/vol63/iss1/21
  24. [24] Hamidi, M., Smarandache, F., & Davneshvar, E. (2022). Spectrum of superhypergraphs via flows. Journal of mathematics, 2022(1), 9158912. https://doi.org/10.1155/2022/9158912
  25. [25] Smarandache, F. (2022). Introduction to the n-superhypergraph-the most general form of graph today. Infinite Study. https://B2n.ir/xe2789
  26. [26] Hamidi, M., & Taghinezhad, M. (2023). Application of superhypergraphs-based domination number in real world. Infinite Study. https://B2n.ir/wp3190
  27. [27] Fujita, T., & Smarandache, F. (2025). A concise study of some superhypergraph classes. Infinite Study. https://B2n.ir/nx6674
  28. [28] Sun, J., Jiang, Q., & Lu, C. (2020). Recursive social behavior graph for trajectory prediction. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 660-669). IEEE. https://doi.org/10.1109/CVPR42600.2020.00074
  29. [29] Zhang, G., Wu, J., Jeon, G., Chen, Y., Wang, Y., & Tan, M. (2023). Revealing social group long-term survival for smart cities based on behavior graph structures using virtual game. IEEE internet of things journal, 10(21), 18733-18744. https://doi.org/10.1109/JIOT.2023.3280568
  30. [30] Yu, X., Li, W., Zhang, C., Wang, J., Zhao, Y., Liu, F., ... ., & Chen, D. (2024). Time-aware multi-behavior graph network model for complex group behavior prediction. Information processing & management, 61(3), 103666. https://doi.org/10.1016/j.ipm.2024.103666
  31. [31] Tian, J., & Zhang, H. (2019). A credible cloud service model based on behavior graphs and tripartite decision-making mechanism. In Cloud security: Concepts, methodologies, tools, and applications (pp. 903-922). IGI Global. https://doi.org/10.4018/978-1-5225-8176-5.ch047
  32. [32] Zhou, Z., Liu, W., Xu, D., Wang, Z., & Zhao, J. (2023). Uncovering the unseen: Discover hidden intentions by micro-behavior graph reasoning. Proceedings of the 31st ACM international conference on multimedia (pp. 6623-6633). Association for computing machinery (ACM). https://doi.org/10.1145/3581783.3611892
  33. [33] Liu, Y., Ren, Z., Zhang, W. N., Che, W., Liu, T., & Yin, D. (2020). Keywords generation improves e-commerce session-based recommendation. Proceedings of The web conference 2020 (pp. 1604-1614). Association for computing machinery (ACM). https://doi.org/10.1145/3366423.3380232
  34. [34] Moreira, G. D. S. P., Rabhi, S., Ak, R., Kabir, M. Y., & Oldridge, E. (2021). Transformers with multi-modal features and post-fusion context for e-commerce session-based recommendation. https://doi.org/10.48550/arXiv.2107.05124
  35. [35] Ali, I., & Melton, A. (2018). Semantic-based text document clustering using cognitive semantic learning and graph theory. 2018 IEEE 12th international conference on semantic computing (ICSC) (pp. 243-247). IEEE. https://doi.org/10.1109/ICSC.2018.00042
  36. [36] Liu, W., Sun, Z., Wei, S., Zhang, S., Zhu, G., & Chen, L. (2024). PS-GCN: Psycholinguistic graph and sentiment semantic fused graph convolutional networks for personality detection. Connection science, 36(1), 2295820. Https://doi.org/10.1080/09540091.2023.2295820
  37. [37] Bonaccorsi, A., Melluso, N., Chiarello, F., & Fantoni, G. (2021). The credibility of research impact statements: A new analysis of REF with Semantic Hypergraphs. Science and public policy, 48(2), 212-225. https://doi.org/10.1093/scipol/scab008
  38. [38] Menezes, T., & Roth, C. (2019). Semantic hypergraphs. https://doi.org/10.48550/arXiv.1908.10784
  39. [39] Nunes, B. P., Kawase, R., Fetahu, B., Dietze, S., Casanova, M. A., & Maynard, D. (2013). Interlinking documents based on semantic graphs. Procedia computer science, 22, 231-240. https://doi.org/10.1016/j.procs.2013.09.099
  40. [40] Lin, S. D., & Chalupsky, H. (2008). Discovering and explaining abnormal nodes in semantic graphs. IEEE transactions on knowledge and data engineering, 20(8), 1039-1052. https://doi.org/10.1109/TKDE.2007.190691
  41. [41] Ambadi, P. S., Basche, K., Koscik, R. L., Berisha, V., Liss, J. M., & Mueller, K. D. (2021). Spatio-semantic graphs from picture description: applications to detection of cognitive impairment. Frontiers in neurology, 12, 795374. https://doi.org/10.3389/fneur.2021.795374
  42. [42] Chiang, D., Drewes, F., Gildea, D., Lopez, A., & Satta, G. (2018). Weighted DAG automata for semantic graphs. Computational linguistics, 44(1), 119-186. https://doi.org/10.1162/COLI_a_00309
  43. [43] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  44. [44] Adlassnig, K. P. (1986). Fuzzy set theory in medical diagnosis. IEEE transactions on systems, man, and cybernetics, 16(2), 260-265. https://doi.org/10.1109/TSMC.1986.4308946
  45. [45] Mordeson, J. N., & Nair, P. S. (2012). Fuzzy graphs and fuzzy hypergraphs (Vol. 46). Physica. https://B2n.ir/xh6965
  46. [46] Jun, Y. B., Hur, K., & Lee, K. J. (2017). Hyperfuzzy subalgebras of bck/bci-algebras. Annals of fuzzy mathematics and informatics, 15(1), 17-28. https://doi.org/10.30948/afmi.2018.15.1.17
  47. [47] Ghosh, J., & Samanta, T. K. (2012). Hyperfuzzy set and hyperfuzzy group. International journal of advanced science and technology, 41, 27-38. https://www.earticle.net/Article/A206708
  48. [48] Hatamleh, R., Al-Husban, A., Zubair, S. A. M., Elamin, M., Saeed, M. M., Abdolmaleki, E., ... ., & Khattak, A. M. (2025). Ai-assisted wearable devices for promoting human health and strength using complex interval-valued picture fuzzy soft relations. European journal of pure and applied mathematics, 18(1), 5523-5523. https://doi.org/10.29020/nybg.ejpam.v18i1.5523
  49. [49] Cuong, B. C., & Kreinovich, V. (2013). Picture fuzzy sets-a new concept for computational intelligence problems. 2013 third world congress on information and communication technologies (WICT 2013) (pp. 1-6). IEEE. https://doi.org/10.1109/WICT.2013.7113099
  50. [50] Torra, V., & Narukawa, Y. (2009). On hesitant fuzzy sets and decision. 2009 IEEE international conference on fuzzy systems (pp. 1378-1382). IEEE. https://doi.org/10.1109/FUZZY.2009.5276884
  51. [51] Torra, V. (2010). Hesitant fuzzy sets. International journal of intelligent systems, 25(6), 529-539. https://doi.org/10.1002/int.20418
  52. [52] Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016). Single valued neutrosophic graphs. Journal of new theory, (10), 86-101. https://dergipark.org.tr/en/pub/jnt/issue/34504/381241
  53. [53] Akram, M., Malik, H. M., Shahzadi, S., & Smarandache, F. (2018). Neutrosophic soft rough graphs with application. Axioms, 7(1). https://doi.org/10.3390/axioms7010014
  54. [54] Martin, N. (2021). Plithogenic SWARA-TOPSIS decision making on food processing methods with different normalization techniques. In Advances in decision making. IntechOpen. https://doi.org/10.5772/intechopen.100548
  55. [55] Sathya, P., Martin, N., & Smarandache, F. (2024). Plithogenic forest hypersoft sets in plithogenic contradiction based multi-criteria decision making. Neutrosophic sets and systems, 73, 668–693. https://fs.unm.edu/nss8/index.php/111/article/view/5118

Downloads

Published

2025-02-27

Issue

Vol. 2 No. 1 (2025): Psychology Nexus

Section

Articles

How to Cite

Fujita, T. (2025). A Hierarchical Hypergraph and Superhypergraph Framework for Semantic and Behavioral Graphs in Psychology and the Social Sciences. Psychology Nexus, 2(1), 23-40. https://doi.org/10.48314/nex.vi.27