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| Reviews: We study a non-growth network model, which bases on the nonlinearpreferential redistributions. There are N communities, each ofwhich is characterized by the quantity ki, which is the number ofthe nodes in the community i. At each time step, two communities i and j are chosen by the probability of μ(ki) and υ(kj), respectively. The community i loses one node, and atthe same time the community j gets the node. The total numbers ofcommunities and nodes all over the networks are conserved. Assumingpower-law kernels with exponents α and β, the networkstructures in stationary states are related to the parameters α and β. We investigate stationary distributions ofthese quantities both analytically and numerically in all cases, andfind that the model exhibits the scaling behavior for some cases.For α>β, the network is widely homogeneous with acharacteristic connectivity. For α<β, the network ishighly heterogeneous with the emergence of condensing phenomenon.Therefore, most of the distribution will be broken in two parts. For α=β and α≥0, along with the increase of α, the network gradually shift form scale free with anexponential cutoff for scale free. For α=β and α<0, the network is non-monotonous. |
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| Keywords:Complex networks; Nonlinear preference; Zipf exponent |
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