Generalized Fuzzy Digraph

Jump To References Section

Authors

  • Department of Mathematics, Vellalar College for Women (Autonomous), Erode – 638012, Tamil Nadu ,IN
  • Department of Mathematics, Vellalar College for Women (Autonomous), Erode – 638012, Tamil Nadu ,IN
  • Department of Mathematics, Vellalar College for Women (Autonomous), Erode – 638012, Tamil Nadu ,IN

DOI:

https://doi.org/10.15613/sijrs/2023/v10i1-2/44914

Keywords:

Centrality, Degree Centrality, Generalized Fuzzy Digraph, Membership Value

Abstract

A tool for portraying several real networks is a fuzzy graph. The fuzzy graphs are merely suitable to depict some networks due to various edge limitations. The expected results of research on a variety of applications remain highly outgoing and might be surpassing. In the present article, we analysed the centrality of the community networks utilizing a Generalized Fuzzy Digraph (GFD) to figure out who make use of the Telegram channel vigorously for the preparation of NET examination. Utilizing the cartesian product the three values are turned into one value for fuzzification, leading to the values to get fuzzified. This paper applies GFD to demonstrate an application to identify the central individual in any social group such as Telegram, Facebook, Instagram etc., which provides a best result in many crucial situations.

Downloads

Published

2024-07-19

 

References

Shimbel A. Structural parameters of communication networks. Bulletin of Mathematical Biophysics. 1953; 15(4):501-7. https://doi.org/10.1007/BF02476438

Freeman LC. Centrality in social networks conceptual clarification. Social Networks. 1978; 1(3):215-39. https://doi.org/10.1016/0378-8733(78)90021-7

Stephenson K, Zelen M. Rethinking centrality: Methods and examples. Social Networks. 1989; 11(1):1-37. https://doi.org/10.1016/0378-8733(89)90016-6

Randes U. A faster algorithm for betweenness centrality*. The Journal of Mathematical Sociology. 2001; 25(2):163–77. https://doi.org/10.1080/0022250X.2001.9990249

Estrada E, Rodríguez-Velázquez JA. Subgraph centrality in complex networks. Physical Review E. 2005; 71(5). https://doi.org/10.1103/PhysRevE.71.056103 PMid:16089598

Rodriguez JA, Estrada E, Gutierrez A. Functional centrality in graphs. Linear and multilinear algebra/Linear and multilinear algebra. 2007; 55(3):293–302. https://doi.org/10.1080/03081080601002221

Bonacich P. Some unique properties of eigenvector centrality. Social Networks. 2007; 29(4):555–64. https://doi.org/10.1016/j.socnet.2007.04.002

Opsahl T, Agneessens F, Skvoretz J. Node centrality in weighted networks. Generalizing degree and shortest paths. Social Networks. 2010; 32(3):245-251.

Joyce KE, Laurienti PJ, Burdette JH, Hayasaka S. A new measure of centrality for brain networks. PLoS ONE. 2010; 5(8). https://doi.org/10.1371/journal.pone.0012200 PMid:20808943 PMCid:PMC2922375

Liu JG, Ren ZM, Guo Q. Ranking the spreading influence in complex networks. Physica A: Statistical Mechanics and its Applications. 2013; 392(18):4154–9. https://doi.org/10.1016/j.physa.2013.04.037

Bae J, Kim S. Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A: Statistical Mechanics and its Applications. 2014; 395:549–59. https://doi.org/10.1016/j.physa.2013.10.047

Liu Y, Tang M, Zhou T, Do Y. Identify influential spreaders in complex networks, the role of neighborhood. Physica A: Statistical Mechanics and its Applications. 2016; 452:289–98. https://doi.org/10.1016/j.physa.2016.02.028

Wang J, Hou X, Li K, Ding Y. A novel weight neighborhood centrality algorithm for identifying influential spreaders in complex networks. Physics A S0378. 2017; 4371(17):30121-8.

Samanta S, Dubey VK, Sarkar B. Measure of influences in social networks. Applied Soft Computing. 20201; 99. https://doi.org/10.1016/j.asoc.2020.106858

Kauffman A. Introduction a le Theorie des Sous-emsembles Flous, Masson et Cie Editeurs, Paris; 1973.

Mahapatra R, Samanta S, Pal M, Lee JG, Khan S, Naseem U, et al. Colouring of COVID-19 affected region based on fuzzy directed graphs. Computers, Materials and Continua. 2021; 68(1):1219–33. https://doi.org/10.32604/cmc.2021.015590

Samanta S, Sarkar B. A study on generalized fuzzy graphs. Journal of Intelligent and Fuzzy Systems. 2018; 35(3):3405-12. https://doi.org/10.3233/JIFS-17285

Zimmermann HJ. Fuzzy set theory and its applications, Fourth Edition; 1934.