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.

26 pages

References in corpus (6)

• Power-law distributions in empirical data
• Hyperbolic Geometry of Complex Networks
• Kronecker Graphs: An Approach to Modeling Networks
• Graph Evolution: Densification and Shrinking Diameters
• Network Cosmology
• Moment based estimation of stochastic Kronecker graph parameters

Cited by in corpus (1)

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