  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 xi 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.
