Random continuous model of scale-free networks

There are a lot of continuous evolving networks in real world, such as Internet, www network, etc. The evolving operation of these networks are not an equating interval of time by chance. In this paper, the author proposes a new mathematical model for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution of which counting process determines the operating number, and has proved that this system self-organizes into scale-free structures with scaling exponent γ = 3+ α/m.