Dimensionality of social networks using motifs and eigenvalues

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Dimensionality of social networks using motifs and eigenvalues

Bonato, Anthony; Gleich, David F; Kim, Myunghwan; Mitsche, Dieter; Prałat, Paweł; Tian, Yanhua; Young, Stephen J

PloS one, 09/2014, Volume: 9, Issue: 9

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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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