One Small-World Scale-Free Network Model Having Tuned Parameters

Two characters, scale-free and hierarchical structure, are shown in lots of real systems all over the world. In this article, firstly, we build up a class of network models with hierarchical structure, denoted by N-h(t), and prove it to he scale-free. By computing average degrees, we find these network models are all sparse. Secondly, based on their special topological structure, we research analytically average distance of each model belonging to N-h(1) and present an iteration computational method of average distance corresponding to every one in N-h(t). Finally, we discuss the affect by changing some tunable parameters to average distance in the set N-h(t), and compare our hierarchical network models with previous ones, and show some meaning problems for gaining more universal methods of computing average distance in hierarchical networks.