Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A dynamical characterization of the small world phase   Small-world (SW) networks have been identified in many different fields.
Topological coefficients like the clustering coefficient and the characteristic
path length have been used in the past for a qualitative characterization of
these networks. Here a dynamical approach is used to characterize the
small-world phenomenon. Using the $\beta -$model, a coupled map dynamical
system is defined on the network. Entrance to and exit from the SW phase are
related to the behavior of the ergodic invariants of the dynamics.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph