| In this article, we first based on the 2-dimensional girdle zone and 2- dimensional sphere triangulation propose a simple rule that generates scale-free networks with very large clustering coefficient. The study of complex networks were intensively focused on plane networks or even Euclidean Space, while, in the paper, we study complex network on the manifold. We obtain the analytical results of power-law exponentγ= 3,In addition, We calculated the clustering coefficient C1 , C2 ,C3 .Secondly, we propose a simple rule that generates scale-free networks .These networks are called Hierarchical Simplex networks(HST) as they can be considered as a variation of these networks .We obtain the analytical results of power-law exponentγ= 2 + 1/d and clustering coefficient C for d -dimensional HST. In addition, The HST posses hierarchical structures as C(k)～k-1, when k>>d ,which is relevance to the observations of many real-world networks.Thirdly, we review briefly the recent discussion in literature about the two infectious diseases models: SIS model and SIR model and the problem of how to calculate the transmission threshold in value of the two models on HST networks. SIS and SIR model can be understood by the mean field theory, and they do not exist nonzero transmission threshold on the HST networks. Scale-free networks, which are characterized by diverging connectivity fluctuations in the limit of a very large number of nodes, have an influence on the epidemic spreading. In particular, the application of complex networks to SIS and SIR spreading research was pointed out.Finally, because of the vanishing epidemic threshold for virus spreading on HST and SNs networks, We find that on this network even weakly infectious viruses can spread and prevail. This vanishing threshold is a consequence of the nodes with a large number of links encoded by the tail of power law P ( k ). In this paper, we cure mostly the highly connected nodes and find this method can restore a finite epidemic threshold. |
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