Scale-free networks by super-linear preferential attachment rule

A network growth model with geographic limitation of accessible information about the status of existing nodes is investigated. In this model, the probability Π(k)Π(k) of an existing node of degree kk is found to be super-linear with Π(k)∼kαΠ(k)∼kα and α>1α>1 when there are links from new nodes. The numerical results show that the constructed networks have typical power-law degree distributions P(k)∼k−γP(k)∼k−γ and the exponent γγ depends on the constraint level. An analysis of local structural features shows the robust emergence of scale-free network structure in spite of the super-linear preferential attachment rule. This local structural feature is directly associated with the geographical connection constraints which are widely observed in many real networks.