  We consider the dimensionality of social networks, and develop experiments
aimed at predicting that dimension. We find that a social network model with
nodes and links sampled from an $m$-dimensional metric space with power-law
distributed influence regions best fits samples from real-world networks when
$m$ scales logarithmically with the number of nodes of the network. This
supports a logarithmic dimension hypothesis, and we provide evidence with two
different social networks, Facebook and LinkedIn. Further, we employ two
different methods for confirming the hypothesis: the first uses the
distribution of motif counts, and the second exploits the eigenvalue
distribution.
