Abstract:

As is well known,most real world networks are not random networks.A few nodes usually have a lot of links while most nodes have few,and it is an important characteristic of scalefree networks,which is an important research topic.In this paper we firstly define a new type of selfgrowing network model, calculate its basic parameters,and validate its scalefree feature.We then prove that the degree distribution of the spanning tree with maximum leaves obeys the power law distribution and we get the balanced set of the network.Through those behaviors,we have a preliminary exploration on scalefree networks.Finally we propose an algorithm to calculate the average path length.

Key words: self-growing network;complex network;spanning trees;scale-free networks;balance set