Scale-free networks on Euclidean lattices

We suggest a method for embedding scale-free networks, with degree
distribution P(k)~k^{-\\lambda}, in regular Euclidean lattices. The embedding is driven by a natural constraint of minimization of the total length of the links in the system. We find that all networks with \\lambda>2 can be successfully embedded up to an (Euclidean) distance x which can be made as large as desired upon the changing of an external parameter. Clusters of
successive chemical shells are found to be compact (the fractal dimension is
d_f=d), while the dimension of the shortest path between any two sites is
smaller than one: d_{min}= (\\lambda-2)/(\\lambda-1-1/d), contrary to all other known examples of fractals and disordered lattices.