Abstract: Growth and preferential attachment are important mechanisms in forming scale-free networks. There are two methods of important preferential attachment: degree preferential attachment and ranking preferential attachment, and two methods of important growing: star-like graph growth and complete graph growth. In this paper, ranking preferential attachment is analyzed to show that it can be used to construct model that have wide range of degree exponent. A new model with motif growth and ranking preferential attachment is then constructed. The model has a wide range of degree exponent, and its clustering coefficient is independent of the network size when the degree exponent is larger than 2.5.

Key words: complete graph growth, degree preferential attachment, motif growth
, ranking preferential attachment, star-like graph growth, scale-free networks