A spatial model for social networks
  We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this model captures many generic properties of social networks, including the ``small-world'' properties, skewed degree distribution, and most distinctively the existence of community structures. 
Ling Heng Wong, Philippa Pattison, Garry Robins