Weighted Scaling in Non-growth Random Networks

CHEN Guang; YANG Xu-Hua; XU Xin-Li

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Communications in Theoretical Physics ›› 2012, Vol. 58 ›› Issue (03) : 456-462.

Interdisciplinary Physics and Related Areas of Science and Technology

Weighted Scaling in Non-growth Random Networks

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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.

Key words

weighted network / random network / non-growth / scale-free distribution

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CHEN Guang, YANG Xu-Hua, XU Xin-Li. Weighted Scaling in Non-growth Random Networks[J]. Communications in Theoretical Physics, 2012, 58(03): 456-462

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Funding

Supported by the National Natural Science Foundation of China under Grant No. 60874080, the Commonweal Application Technique Research Project of Zhejiang Province under Grant No. 2012C2316 and the Open Project of State Key Lab of Industrial Control Technology of Zhejiang University under Grant No. ICT1107