Dimensionality of Social Networks Using Motifs and Eigenvalues

Abstract : 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.
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PLoS ONE, Public Library of Science, 2014, 〈10.1371/journal.pone.0106052.s001〉
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Anthony Bonato, David Gleich, Myunghwan Kim, Dieter Mitsche, Pawel Pralat, et al.. Dimensionality of Social Networks Using Motifs and Eigenvalues. PLoS ONE, Public Library of Science, 2014, 〈10.1371/journal.pone.0106052.s001〉. 〈hal-01291958〉

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