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. 
Tanya Araujo, R. Vilela Mendes and Jo\~ao Seixas