Random Connection Based Scale-free Networks

Scale-free phenomenon has opened up a new network model as a special form of degree distribution. Preferential connection and growth constitutive are generally considered as the tow key factors in the formation of scale-free network. However, some network model with completely random connections instead of preferential connection can also generate scale-free networks, such as the protein interaction network in a cell. The article constructed such a random connection way: select an arbitrary neighbor vertex of a random vertex to add side. Through our simulation shows this model absolutely has the characteristics of scale-free networks. And the power-law distribution index [1+β^(-1)] of the new model is related to m which is the number of add edges every time. When m is sufficiently large, [1+β^(-1)] tends to quickly stable and the final size is 3. Then we use the Mean field theory analyzed theoretically, and get an analytic solution of degree distribution. Our study reveals that random connections without preferential strategy can also generate scale-free network.