Based on the “classic” scale-free network model

  the network growth principle(preferential attachment mechanism) is extended. Starting from a more general situation

some vertex-preferential attachment probability in different constraint conditions are established

and then the partial differential equation satisfied a more general network dynamic system is set up

and also another important topological property of scale-free network is found. Then a much realistic preferential attachment probability is presented. Finally

a more general network model is generated. By discussing its scale-free property

that scale-free parameter γ ranges from 1 to 4 is captured.