Knowing a network by walking on it: emergence of scaling

Abstract

A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two limiting cases and numerical simulations the phase diagram of the model is obtained. In the stationary limit, large network sizes, a phase transition from a network with finite average connectivity to a network with a power law distribution of connectivities, with no finite average, is found. Results are compared with measurements on real networks.