Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale-free Networks on Lattices   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.

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex