  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.
