ScaleFree Networks on Lattices
Abstract
We suggest a method for embedding scalefree networks, with degree distribution P(k)~k^{λ}, in regular Euclidean lattices accounting for geographical properties. 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 λ>2 can be successfully embedded up to a (Euclidean) distance ξ 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 1: d_{min}=(λ2)/(λ11/d), contrary to all other known examples of fractals and disordered lattices.
 Publication:

Physical Review Letters
 Pub Date:
 November 2002
 DOI:
 10.1103/PhysRevLett.89.218701
 arXiv:
 arXiv:condmat/0205613
 Bibcode:
 2002PhRvL..89u8701R
 Keywords:

 89.75.Hc;
 05.50.+q;
 89.75.Da;
 Networks and genealogical trees;
 Lattice theory and statistics;
 Systems obeying scaling laws;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 Latex, 4 pages, 5 figures