A geometric model for on-line social networks

We study the link structure of on-line social networks (OSNs), and introduce a new model for such networks which may help infer their hidden underlying reality. In the geo-protean (GEO-P) model for OSNs nodes are identified with points in Euclidean space, and edges are stochastically generated by a mixture of the relative dis-tance of nodes and a ranking function. With high prob-ability, the GEO-P model generates graphs satisfying many observed properties of OSNs, such as power law degree distributions, the small world property, densifica-tion power law, and bad spectral expansion. We intro-duce the dimension of an OSN based on our model, and examine this new parameter using actual OSN data. We discuss how the dimension parameter of an OSN may eventually be used as a tool to group users with similar attributes using only the link structure of the network. 1