Social Network Models

Three models are often invoked to capture the structure of social networks: (i) Erdos-Renyi random graphs (which are tractable for theoretical analysis), (ii) small-world constructions, and (iii) multi-scale (or scale-free) graphs constructed with preferential attachments of new nodes. We show that none of these three choices are adequate models by themselves, and suggest an alternative, which is a relatively simple modification of the preferential attachment construction.