Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Apollonian Networks   In this letter, we propose a simple rule that generates scale-free networks
with very large clustering coefficient and very small average distance. These
networks are called {\bf Random Apollonian Networks}(RANs) as they can be
considered as a variation of Apollonian networks. We obtain the analytic result
of power-law exponent $\gamma =3$ and clustering coefficient
$C={46/3}-36\texttt{ln}{3/2}\approx 0.74$, which agree very well with the
simulation results. We prove that the increasing tendency of average distance
of RAN is a little slower than the logarithm of the number of nodes in RAN.
Since many real-life networks are both scale-free and small-world, RANs may
perform well in mimicking the reality. The epidemic spreading process is also
studied, we find that the diseases spread slower in RANs than BA networks in
the early stage of SI process, indicating that the large clustering coefficient
may slower the spreading velocity especially in the outbreaks.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con