Random pseudofractal scale-free networks with small-world effect

A random pseudofractal network (RPN) is generated by a recursive growing rule. The RPN is of the scale-free feature and small-world effect. We obtain the theoretical results of power-law exponent γ=3, clustering coefficient C=3π2-19≈ 0.74, and a proof that the mean distance increases no faster than ln N, where N is the network size. These results agree with the numerical simulation very well. In particular, we explain the property of growth and preferential attachment in RPNs. And the properties of a class of general RPNs are discussed in the end.