\input zb-basic \input zb-ioport \iteman{io-port 06080626} \itemau{Zhang, Longteng; Chen, Qinghua} \itemti{A model of the weighted networks with the preferential growth of weights.} \itemso{Appl. Math. Sci., Ruse 6, No. 1-4, 63-68 (2012).} \itemab Summary: A model for the weighted networks is proposed. The model is based on the preferential growth of weights. By mean-field theory, the distributions of the strength and weight for the network are provided and the analytical results show that each distribution has a power-law tail. \itemrv{~} \itemcc{} \itemut{weighted networks; strength distribution; weight distribution; power-law tail} \itemli{http://www.m-hikari.com/ams/ams-2012/ams-1-4-2012/index.html} \end