A Scale-free network is defined by a power-law degree distribution. Let’s consider d the degree of a vertex of a network. If we have a power law, we get: P(d)∼d^-a. If a < 2 then the average degree diverges. If a < 3 then the standard deviation of the degree diverges. Their name is due to the fact that they do not possess a characterization degree and there for scale. We call the vertices with high degree, hubs. A consequence of their structure is that scale-free networks are robust which means that they are resistant to accidental failures i.e random attacks. On the opposite they are more vulnerable than random graphs, to deliberate attacks, sabotage and viruses. This property is useful for the brain and the problem can be solved with its plasticity. Another important property is the short average path lengths. As a global consequence with scale – free networks we can get small world networks. In other words, our brain can be a small world which has in its mind the big world.