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, D. F., Kim, M., Mitsche, D., Prałat, P., Tian, Y., & Young, S. J. (2014). Dimensionality of social networks using motifs and eigenvalues. PLoS ONE, 9(9). https://doi.org/10.1371/journal.pone.0106052