Friendship network image

• Scale free: It is difficult to say it without looking to the distribution of the number of links coming out of any single point. If this distribution follows a power law  $P(k) \sim k^{-c}$, then, we can say that the network is scale free. For the Barabassi & Adler scale free networks the constant c is between 2 and 3. Well, this is difficult to say looking to the diagram, but another curious property of these networks is that the number of links per node looks like a fractal, meaning that if you erase the nodes with highest number of links the remaining nodes maintain the link connectivity architecture (the overall aspect of the network). A consequence of that: the distribution of links coming out of a node (what is called the degree of the node) is a heavy tail distribution, that is, it is quite possible to have nodes with very, very small number of links and with very big, big numbers as well. In contrast, with the light tail distributions where it is impossible to have so small and big values (for example, the human heights distribution is light tail as it is impossible to find people  10 m tall or 10 cm tall, but, curiously 🙂 the richness distribution is heavy tail, I don’t need to give examples….)