Dimensionality of Social Networks Using Motifs and Eigenvalues

Anthony Bonato (1) , David Gleich (2) , Myunghwan Kim (3) , Dieter Mitsche (4) , Pawel Pralat (1) , Amanda Tian (1) , Stephen Young (5)

1 Department of Mathematics [Ryerson University - Toronto]
2 Purdue University [West Lafayette]
3 Stanford University
4 UNS - Université Nice Sophia Antipolis (1965 - 2019)
5 University of Louisville

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.

Domaines: Réseaux et télécommunications [cs.NI]; Mathématique discrète [cs.DM]

Anthony Bonato, David Gleich, Myunghwan Kim, Dieter Mitsche, Pawel Pralat, et al.. Dimensionality of Social Networks Using Motifs and Eigenvalues. PLoS ONE, 2014, ⟨10.1371/journal.pone.0106052.s001⟩. ⟨hal-01291958⟩