Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering and the hyperbolic geometry of complex networks   Clustering is a fundamental property of complex networks and it is the
mathematical expression of a ubiquitous phenomenon that arises in various types
of self-organized networks such as biological networks, computer networks or
social networks. In this paper, we consider what is called the global
clustering coefficient of random graphs on the hyperbolic plane. This model of
random graphs was proposed recently by Krioukov et al. as a mathematical model
of complex networks, under the fundamental assumption that hyperbolic geometry
underlies the structure of these networks. We give a rigorous analysis of
clustering and characterize the global clustering coefficient in terms of the
parameters of the model. We show how the global clustering coefficient can be
tuned by these parameters and we give an explicit formula for this function.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys