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| In this paper, we investigate a class of generalized weightedscale-free networks, where the new vertex connects to $m$ pairs ofvertices selected preferentially. The key contribution of this paperis that, from the standpoint of random processes, we providerigorous analytic solutions for the steady state distributions,including the vertex degree distribution, the vertex strengthdistribution and the edge weight distribution, and we also discussthe clustering coefficient of the model. Numerical simulationsindicate that this network model yields three power lawdistributions for the vertex degrees, vertex strengths and edgeweights, respectively. |
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| Keywords:complex networks; weighted networks; scale-free; degree distribution |
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