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.
Bonato A, Gleich DF, Kim M, Mitsche D, Prałat P, Tian Y, et al. (2014) Dimensionality of Social Networks Using Motifs and Eigenvalues. PLoS ONE 9(9): e106052.