Dimensionality of social networks using motifs and eigenvalues

PLoS One. 2014 Sep 4;9(9):e106052. doi: 10.1371/journal.pone.0106052. eCollection 2014.


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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Computer Graphics
  • Humans
  • Mathematical Concepts
  • Models, Theoretical
  • Social Networking*
  • Support Vector Machine

Grant support

NSERC DG grants; NSF CAREER award CCF-1149756; MITACS for hosting the authors' research team at the Advances in Network Analysis and its Applications Workshop held at the University of British Colombia in July 2012. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.