TY - JOUR
T1 - Scale-Free Networks on Lattices
AU - Rozenfeld, Alejandro F.
AU - Cohen, Reuven
AU - ben-Avraham, Daniel
AU - Havlin, Shlomo
PY - 2002/11/18
Y1 - 2002/11/18
N2 - We suggest a method for embedding scale-free networks, with degree distribution [Formula presented], 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 [Formula presented] can be successfully embedded up to a (Euclidean) distance [Formula presented] 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 [Formula presented]), while the dimension of the shortest path between any two sites is smaller than 1: [Formula presented], contrary to all other known examples of fractals and disordered lattices.
AB - We suggest a method for embedding scale-free networks, with degree distribution [Formula presented], 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 [Formula presented] can be successfully embedded up to a (Euclidean) distance [Formula presented] 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 [Formula presented]), while the dimension of the shortest path between any two sites is smaller than 1: [Formula presented], contrary to all other known examples of fractals and disordered lattices.
UR - http://www.scopus.com/inward/record.url?scp=18744363677&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.89.218701
DO - 10.1103/PhysRevLett.89.218701
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C2 - 12443452
AN - SCOPUS:18744363677
SN - 0031-9007
VL - 89
JO - Physical Review Letters
JF - Physical Review Letters
IS - 21
ER -