Strength of connectedness in fuzzy bunch graphs and fuzzy bunch hypergraphs: A new approach

Document Type : Research Paper

Authors

1 1Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia

2 2,3Research Center of Performance and Productivity Analysis, Istinye University, 34320 Istanbul, Turkey

3 2Department of Technical Sciences, Western Caspian University, 1001 Baku, Azerbaijan

4 2Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, WB 721636, India

5 3Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

6 4College of Engineering and Technology, American University of the Middle East, 54200 Egaila, Kuwait

10.22111/ijfs.2026.9914

Abstract

The existing strength of connectedness in fuzzy graph theory is a max–min quantity. According to this definition, the
strength of a path is the membership of its weakest edge, and the connectedness between two vertices is the maximum
such bottleneck over all paths. That definition is exact for systems in which the weakest edge is the only controlling
factor, but it is too rigid when cumulative route quality matters as well. In this paper we adopt a new notion in which
the strength of a simple path is a convex combination of its bottleneck and its average edge membership. The new
framework defined in this paper for the strength of connectedness is successfully applicable to systems where the classical bottleneck constraint is significant, as well as to systems where the cumulative effects of all edge constraints are more significant than just the bottleneck constraint. Capacity or bandwidth constraints in a network rely only on the weakest (bottleneck) edge, whereas speed, latency, or smoothness constraints have cumulative effects on the entire path from the source to the destination hub in a network. We develop the corresponding theory for fuzzy bunch graphs and fuzzy bunch hypergraphs, that is, grouped fuzzy structures in which vertices are partitioned into bunches and higher-order relations may occur across bunches.

Keywords

References

[1] F. Battiston, et al., Networks beyond pairwise interactions: Structure and dynamics, Physics Reports, 874 (2020),
1-92.
[2] F. Battiston, et al., The physics of higher-order interactions in complex systems, Nature Physics, 17(10) (2021),
1093-1098. https://doi.org/10.1038/s41567-021-01371-4
[3] R. S. Bhadoria, S. Samanta, Y. Pathak, P. K. Shukla, A. A. Zubi, M. Kaur, Bunch graph based dimensionality
reduction using auto-encoder for character recognition, Multimedia Tools and Applications, 81(22) (2022), 32093-32115.
https://doi.org/10.1007/s11042-022-12907-y
[4] K. R. Bhutani, A. Rosenfeld, Strong arcs in fuzzy graphs, Information Sciences, 152 (2003), 319-322. https:
//doi.org/10.1016/S0020-0255(02)00411-5
[5] D. Bilbao, H. Aimar, P. Torterolo, D. M. Mateos, Higher-order interaction analysis via hypergraph models for studying
multidimensional neuroscience data, Biomedical Signal Processing and Control, 112 (2024). https://doi.org/10.
1016/j.bspc.2025.108564
[6] M. Binu, S. Mathew, J. N. Mordeson, Connectivity index of a fuzzy graph and its application to human trafficking,
Fuzzy Sets and Systems, 360 (2019), 117-136. https://doi.org/10.1016/j.fss.2018.06.007
[7] M. Binu, S. Mathew, J. N. Mordeson, Connectivity status of fuzzy graphs, Information Sciences, 573 (2021), 382-395.
https://doi.org/10.1016/j.ins.2021.05.068
[8] S. H. Kundu, K. Das, K. M. Das, L. Mrsic, A. Kalampakas, Fuzzy bunch graphs and properties, International Journal
of Fuzzy Logic and Intelligent Systems, 25(3) (2025), 326-342. https://doi.org/10.5391/IJFIS.2024.25.3.326
[9] R. Lambiotte, M. Rosvall, I. Scholtes, From networks to optimal higher-order models of complex systems, Nature
Physics, 15 (2019), 313-320. https://doi.org/10.1038/s41567-019-0459-y
[10] S. Mathew, M. S. Sunitha, Types of arcs in a fuzzy graph, Information Sciences, 179(11) (2009), 1760-1768.
https://doi.org/10.1016/j.ins.2009.01.003
[11] T. Pramanik, R. Mahapatra, T. Allahviranloo, L. Mrsic, A. Kalampakas, S. Samanta, Spherical fuzzy hypergraph in
decision making, Scientific Reports, 16 (2026). https://doi.org/10.1038/s41598-026-44917-3
[12] A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press,
(1975), 77-95. https://doi.org/10.1016/B978-0-12-775260-0.50008-6
13] S. Samanta, V. K. Dubey, K. Das, Coopetition bunch graphs: Competition and cooperation on COVID-19 research,
Information Sciences, 589 (2022), 1-33. https://doi.org/10.1016/j.ins.2021.12.025
[14] S. Samanta, V. K. Dubey, A. Kalampakas, Structural and coloring techniques of generalized bunch graphs, (2026).
https://doi.org/10.13140/RG.2.2.35644.81285
[15] L. Torres, A. S. Blevins, D. S. Bassett, T. Eliassi-Rad, The why, how, and when of representations for complex
systems, SIAM Review, 63(3) (2021), 435-485. https://doi.org/10.1137/20M1355896
[16] Y. Zhang, M. Lucas, F. Battiston, Higher-order interactions shape collective dynamics differently in hypergraphs and
simplicial complexes, Nature Communications, 14 (2023), 1605. https://doi.org/10.1038/s41467-023-37190-9
Iranian Journal of Fuzzy Systems
Volume 23, Issue 3
May and June 2026
Pages 69-84

Files

Share

How to cite

Statistics