Dynamical Random Graphs

Tatyana Turova



Abstract:

Randomly grown networks became a subject of intensive studies over the
last few years. Examples of such systems are ranged from the artificial
structures as world wide web, social networks to the biological neural
networks. We investigate a
general model which provides a bridge between randomly grown graphs  and
the classical random graphs.  Introducing a class of dynamical graphs
with a memory allows us to obtain a unified overview on rather different

models and the relations between them.
We find the critical values of the parameters at which our model
exhibits phase
transitions and describe the properties of the phase diagram.
Finally, we compare and discuss the efficiency of the corresponding
networks.