title: 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.
authors.affiliation: Department of Mathematics, Ryerson University, Toronto, Ontario, Canada.
authors.forename: Anthony
authors.initials: A
authors.lastname: Bonato
authors.affiliation: Computer Science Department, Purdue University, West Lafayette, Indiana, United States of America.
authors.forename: David F
authors.initials: DF
authors.lastname: Gleich
authors.affiliation: Electrical Engineering Department, Stanford University, Stanford, California, United States of America.
authors.forename: Myunghwan
authors.initials: M
authors.lastname: Kim
authors.affiliation: Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, Nice, France.
authors.forename: Dieter
authors.initials: D
authors.lastname: Mitsche
authors.affiliation: Department of Mathematics, Ryerson University, Toronto, Ontario, Canada.
authors.forename: Paweł
authors.initials: P
authors.lastname: Prałat
authors.affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada.
authors.forename: Yanhua
authors.initials: Y
authors.lastname: Tian
authors.affiliation: Mathematics Department, University of Louisville, Louisville, Kentucky, United States of America.
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Young
mesh_terms: D003196:Computer Graphics; D006801:Humans; D055641:Mathematical Concepts; D008962:Models, Theoretical; D060756:Social Networking; D060388:Support Vector Machine