  Scale-free networks constitute a fast-developing field that has already
provided us with important tools to understand natural and social phenomena.
From biological systems to environmental modifications, from quantum fields to
high energy collisions, or from the number of contacts one person has, on
average, to the flux of vehicles in the streets of urban centres, all these
complex, non-linear problems are better understood under the light of the
scale-free network's properties. A few mechanisms have been found to explain
the emergence of scale invariance in complex networks. Here we discuss a
mechanism based on how information is locally spread among agents in a
scale-free network. We show that the correct description of the information
dynamics is given in terms of the q-exponential function, with the power-law
behaviour arising in the asymptotic limit. This result shows that the best
statistical approach to the information dynamics is given by Tsallis
Statistics. We discuss the main properties of the information spreading process
in the network and analyse the role and behaviour of some of the parameters as
the number of agents increases. The different mechanisms for optimization of
the information spread are discussed.
