Communication Networks with an Emergent Dynamical Structure

A model with a dynamical network structure is studied. The essential difference from other models is that a disappearance of links is also allowed. The obtained results suggest that under certain conditions a fairly robust cluster, which contains all of the elements of the system, can be formed. According to the power law dependence in the node connectivity distribution, a scale-free regime can occur in such models. The average network diameter behaves as $K^{-\tau }$. The emergent structure is close to the small-world networks for certain values of $p$ and to the large-world ones for others. Generally, the influence of the parameter $K$ on the average network diameter is more significant than that of the system size.