Scale-Free Networks on Lattices
Abstract
We suggest a method for embedding scale-free 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 df=d), while the dimension of the shortest path between any two sites is smaller than 1: dmin=(λ-2)/(λ-1-1/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:cond-mat/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
- E-Print:
- Latex, 4 pages, 5 figures