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.
- Publication:
-
PLoS ONE
- Pub Date:
- September 2014
- DOI:
- 10.1371/journal.pone.0106052
- arXiv:
- arXiv:1405.0157
- Bibcode:
- 2014PLoSO...9j6052B
- Keywords:
-
- Computer Science - Social and Information Networks;
- Physics - Physics and Society
- E-Print:
- 26 pages