Noussaima El.  Khattabi, Fouad  Yakoubi, Mohamed El.  Marraki, 
    The Reliability of Small World Network,
    Journal of Engineering and Applied Sciences,
    Volume 14,Issue 10,
    2019,
    Pages 3260-3265,
    ISSN 1816-949x,
    jeasci.2019.3260.3265,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2019.3260.3265)
    Abstract: The asymptotic spanning tree entropy is a natural measure related to topological and dynamic properties of networks, namely their reliability. However, computing the number of spanning trees of networks using classical algebraic methods is very demanding tasks on term computational resources and time, especially for large networks such as complex networks. In this study, we give an analytic formula for the number of spanning trees and the asymptotic entropy of two type of small-world networks G<sub>k</sub> and C<sub>k</sub> by using two methods of decomposition based on geometrical transformation which are Bipartite method and Reduction method. Then, we estimate and compare the robustness level of the networks G<sub>k</sub> and C<sub>k</sub> that have the same average degree of nodes.
    Keywords: Number of spanning trees;asymptotic entropy;network reliability;complex network;small world
network;bipartite method;reduction method