Open AccessDimensionality of Social Networks Using Motifs and Eigenvalues
Author(s) -
Anthony Bonato,
David F. Gleich,
Myunghwan Kim,
Dieter Mitsche,
Paweł Prałat,
Amanda Tian,
Stephen G. Young
Publication year - 2014
Publication title -
hal (le centre pour la communication scientifique directe)
Language(s) - English
DOI - 10.1371/journal.pone.0106052.s001
Subject(s) - curse of dimensionality , eigenvalues and eigenvectors , artificial intelligence , computer science , pattern recognition (psychology) , mathematics , physics , quantum mechanics
International audienceWe 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