Dynamic weight evolution network with preferential attachment

A dynamic weight evolution network with preferential attachment is introduced. The network includes two significant characteristics. (i) Topological growth: triggered by newly added node with M links at each time step, each new edge carries an initial weight growing nonlinearly with time. (ii) Weight dynamics: the weight between two existing nodes experiences increasing or decreasing in a nonlinear way. By using continuum theory and mean-field method, we study the strength, the degree, the weight and their distributions. We find that the distributions exhibit a power-law feature. In particular, the relationship between the degree and the strength is nonlinear, and the power-law exponents of the three are the same. All the theoretical predictions are successfully contrasted with numerical simulations.