  Social movements, neurons in the brain or even industrial suppliers are best
described by agents evolving on networks with basic interaction rules. In these
real systems, the connectivity between agents corresponds to the a critical
state of the system related to the noise of the system. The new idea is that
connectivity adjusts itself because of two opposite tendencies: on the one hand
informations percolation is better when the network connectivity is small but
all agents have rapidely the same state and the dynamics stops.
  On the other hand, when agents have a large connectivity, the state of a node
(opinion of a person, state of a neuron, ...) tends to freeze: agents find
always a minority among their neighbours to support their state. The model
introduced here captures this essential feature showing a clear transition
between the two tendencies at some critical connectivity. Depending on the
noise, the dynamics of the system can only take place at a precise critical
connectivity since, away from this critical point, the system remains in a
static phase. When the noise is very small, the critical connectivity becomes
very large, and highly connected networks are obtained like the airports
network and the Internet. This model may be used as a starting point for
understanding the evolution of agents living on networks.
