Topology and correlations in structured scale-free networks

We study a recently introduced class of scale-free networks showing a high clustering coefficient and nontrivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small-world properties in the whole parameter range. We discuss the physical properties of these networks in the light of the present detailed analysis.