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Extensive studies have been done to understand the principles behindarchitectures of real networks. Recently, evidences for hierarchicalorganization in many real networks have also been reported. Here, we present anew hierarchical model which reproduces the main experimental propertiesobserved in real networks: scale-free of degree distribution $P(k)$ (frequencyof the nodes that are connected to $k$ other nodes decays as a power-law$P(k)\sim k^{-\gamma}$) and power-law scaling of the clustering coefficient$C(k)\sim k^{-1}$. The major novelties of our model can be summarized asfollows: {\it (a)} The model generates networks with scale-free distributionfor the degree of nodes with general exponent $\gamma > 2$, and arbitrarilyclose to any specified value, being able to reproduce most of the observedhierarchical scale-free topologies. In contrast, previous models can not obtainvalues of $\gamma > 2.58$. {\it (b)} Our model has structural flexibilitybecause {\it (i)} it can incorporate various types of basic building blocks(e.g., triangles, tetrahedrons and, in general, fully connected clusters of $n$nodes) and {\it (ii)} it allows a large variety of configurations (i.e., themodel can use more than $n-1$ copies of basic blocks of $n$ nodes). Thestructural features of our proposed model might lead to a better understandingof architectures of biological and non-biological networks.Comment: RevTeX, 5 pages, 4 figure

Flexible construction of hierarchical scale-free networks with general exponent