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Weighted Scaling in Non-growth Random Networks
Authors:CHEN Guang  YANG Xu-Hua  XU Xin-Li
Institution:College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China
Abstract:We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.
Keywords:weighted network  random network  non-growth  scale-free distribution  
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