Stationary State Structure of a Random Copying Mechanism over a Complex Network

An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary regime in which the distribution of states is independent of the degree. The effects of network topology on the process are characterized introducing a quantity called influence and studying its behavior for scale-free and random networks. We show that for this model degree averaged quantities are constant in time regardless of the number of states involved.