Scale-free Networks on Lattices

Details Scale-free Networks on Lattices Scale-free Networks on Lattices

2002-05-29

arxiv.org/abs/cond-mat/0205613v1

Phys. Rev. Lett. 89, 218701 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Latex, 4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.89.218701

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.

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