Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-size scaling of geometric renormalization flows in complex
  networks   Recently, the concept of geometric renormalization group provides a good
approach for studying the structural symmetry and functional invariance of
complex networks. Along this line, we systematically investigate the
finite-size scaling of structural and dynamical observables in geometric
renormalization flows of synthetic and real evolutionary networks. Our results
show that these observables can be well characterized by a certain scaling
function. Specifically, we show that the critical exponent implied by the
scaling function is independent of these observables but only depends on the
small-world properties of the network, namely, all networks located in the
small-world phase have a uniform scaling exponent, while those located in the
non-small-world phase and in their critical regions have another uniform
scaling. More importantly, we perform extensive experiments on real
evolutionary networks with small-world characteristics, and our results show
that these observables also have uniform scaling in their geometric
renormalization flows. Therefore, in a sense this exponent can be used as an
effective measure for classifying universal small-world and non-small-world
network models.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn