Abstract: Causes of two classes of scale-free networks are analyzed. A scale-free network evolution model is proposed and a series of numerical experiments are carried out. Theoretical analysis and numerical experiments show that if network density is sparse and stable enough, a persistently stable scale-free network can be produced by degree-based preferential attachment. Growth of network size as well as addition and deletion of vertices and edges are objective realities. They have the function of controlling network density as well. A sufficiently sparse density and degree-based preferential attachment are common necessities of scale-free networks. This deduction can be used to explain reasonably the cause of growing and non-growing scale-free networks. The results are helpful in understanding diversified real scale-free networks and design of corresponding models.

Key words: growing networks, non-growing networks, scale-free networks, preferential attachment, network density