Stability of structured networks
It is known from the Wigner-May stability theorem that for a random network
with N nodes, connectivity C and where the weights of the links are normally
distributed with mean 0 and variance 
- the probability of linear stability of the network around one of its
many equilibria is given by Z = 
.
Namely if Z > 0, the network is almost certainly stable, and if Z <
0, the network is almost certainly unstable.
What is a small-world network ?
