Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering under the line graph transformation: Application to reaction
  network   Many real networks can be understood as two complementary networks with two
kind of nodes. This is the case of metabolic networks where the first network
has chemical compounds as nodes and the second one has nodes as reactions. The
second network can be related to the first one by a technique called line graph
transformation (i.e., edges in an initial network are transformed into nodes).
Recently, the main topological properties of the metabolic networks have been
properly described by means of a hierarchical model. In our work, we apply the
line graph transformation to a hierarchical network and the clustering
coefficient $C(k)$ is calculated for the transformed network, where $k$ is the
node degree. While $C(k)$ follows the scaling law $C(k)\sim k^{-1.1}$ for the
initial hierarchical network, $C(k)$ scales weakly as $k^{0.08}$ for the
transformed network. These results indicate that the reaction network can be
identified as a degree-independent clustering network.

33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess