Literature: Scale Free Networks from Self-Organisation

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks on the network. The algorithm uses only local graph information so this is a process of self-organisation. We demonstrate that this result holds for a wide range of parameters of the walk algorithm. We show that the standard mean field equations are an excellent approximation to the real networks we grow, but that fall short of a true scale-free network when the number of vertices is one million or smaller. We also generalise the random walk algorithm to produce weighted networks with power law distributions of both weight and degree. We suggest that a random walk self-organisation mechanism lies behind the many scale-free networks found in the real world.