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 be 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 (t) 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.