Multistage random growing small-world networks with power-law degree distribution

We present a simple rule which could generate scale-free networks with very large clustering coefficient and very small average distance. These networks, called the multistage random growing networks (MRGNs), are constructed by a two-stage adding process for each new node. The analytic results of the power-law exponent y = 3 and the clustering coefficient C = 0.81 are obtained, which agree with the simulation results approximately. In addition, we find that the average distance of the networks increases logarithmically with the network size, which is consistent with the theoretical predictions. Since many real-world networks are both scale-free and small-world, the MRGNs may perform well in mimicking reality.