Topological Properties of Four-Layered Neural Networks

M. Javaid 1 , M. Abbas 2 , Jia-Bao Liu 3 , W. C. Teh 4 ,  and Jinde Cao 5
  • 1 Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan
  • 2 Department of Mathematics, GC University, 54000, Lahore, Pakistan
  • 3 School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China
  • 4 School of Mathematical Sciences, Universiti Sains, Malaysia
  • 5 School of Mathematics, Southeast University, 210096, Nanjing, China


A topological property or index of a network is a numeric number which characterises the whole structure of the underlying network. It is used to predict the certain changes in the bio, chemical and physical activities of the networks. The 4-layered probabilistic neural networks are more general than the 3-layered probabilistic neural networks. Javaid and Cao [Neural Comput. and Applic., DOI 10.1007/s00521-017-2972-1] and Liu et al. [Journal of Artificial Intelligence and Soft Computing Research, 8(2018), 225-266] studied the certain degree and distance based topological indices (TI’s) of the 3-layered probabilistic neural networks. In this paper, we extend this study to the 4-layered probabilistic neural networks and compute the certain degree-based TI’s. In the end, a comparison between all the computed indices is included and it is also proved that the TI’s of the 4-layered probabilistic neural networks are better being strictly greater than the 3-layered probabilistic neural networks.

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