On the Topological Properties of the Certain Neural Networks

Jia-Bao Liu 1 , 2 , Jing Zhao 2 , Shaohui Wang 3 , M. Javaid 4 ,  and Jinde Cao 5
  • 1 School of Mathematics, Southeast University, Nanjing, , Jiangsu, China
  • 2 School of Mathematics and Physics, Anhui Jianzhu University, , Hefei, China
  • 3 Department of Mathematics, Savannah State University, , Savannah, USA
  • 4 Department of Mathematics, School of Science, University of Management and Technology, , Lahore, Pakistan
  • 5 School of Mathematics, Southeast University, Nanjing, , Jiangsu, China

Abstract

A topological index is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. In [Javaid and Cao, Neural Computing and Applications, DOI 10.1007/s00521-017-2972-1], the various degree-based topological indices for the probabilistic neural networks are studied. We extend this study by considering the calculations of the other topological indices, and derive the analytical closed formulas for these new topological indices of the probabilistic neural network. Moreover, a comparative study using computer-based graphs has been carried out first time to clarify the nature of the computed topological descriptors for the probabilistic neural networks. Our results extend some known conclusions.

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