A Class of Scale-free Network Model with the Degree Sequence of Geometric Sequence

摘要

A new network model with the degree sequence of geometric sequence is proposed in this paper. The network model is theoretically proved to be a scale-free network, the power exponent of which is simultaneously obtained. The degree sequence of the network model is a geometric sequence, the first term of which is a positive integer, and common ratio q of which is a positive integer greater than 1. The length of the degree sequence is l. The number of nodes with k_i degree is b~(n-i+1), and the power exponent is log_q b, where 6 is also a positive integer, and n = l - 1. In the network model, the geometric sequence is used to determine network parameters, such as power exponent, the minimum degree and the number of nodes. Subsequently, related properties of the network are analyzed. Then, the topology structure of the network is found to vary with the change of degree sequence length. However, the scale-free property of it is always the same. Finally, some instances are employed to illustrate the network model. The illustrations show that the network model may exhibit different network structures.