Emergence of a small world from local interactions: Modeling acquaintance networks

How does one make acquaintances? A simple observation from everyday experience is that often one of our acquaintances introduces us to one of his acquaintances. Such a simple triangle interaction may be viewed as the basis of the evolution of many social networks. Here, it is demonstrated that this assumption is sufficient to reproduce major non-trivial features of social networks: Short path length, high clustering, and scale-free or exponential link distributions.