We present a dynamical model for rewiring and attachment in bipartite networks. Edges are placed between nodes that belong to catalogs that can either be fixed in size or growing in size. The model is motivated by an empirical study of data from the video rental service Netflix, which invites its users to give ratings to the videos available in its catalog. We find that the distribution of the number of ratings given by users and that of the number of ratings received by videos both follow a power law with an exponential cutoff. We also examine the activity patterns of Netflix users and find bursts of intense video-rating activity followed by long periods of inactivity. We derive ordinary differential equations to model the acquisition of edges by the nodes over time and obtain the corresponding time-dependent degree distributions. We then compare our results with the Netflix data and find good agreement. We conclude with a discussion of how catalog models can be used to study systems in which agents are forced to choose, rate, or prioritize their interactions from a large set of options.
Skip Nav Destination
Article navigation
December 2010
Research Article|
October 08 2010
Competition for popularity in bipartite networks
Mariano Beguerisse Díaz;
Mariano Beguerisse Díaz
a)
1Centre for Integrative Systems Biology,
Imperial College London
, South Kensington Campus, London SW7 2AZ, United Kingdom
2Division of Biology,
Imperial College London
, South Kensington Campus, London SW7 2AZ, United Kingdom
Search for other works by this author on:
Mason A. Porter;
Mason A. Porter
b)
3Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute,
University of Oxford
, OX1 3LB, United Kingdom
4CABDyN Complexity Centre,
University of Oxford
, OX1 1HP, United Kingdom
Search for other works by this author on:
Jukka-Pekka Onnela
Jukka-Pekka Onnela
c)
4CABDyN Complexity Centre,
University of Oxford
, OX1 1HP, United Kingdom
5Department of Physics,
University of Oxford
, OX1 3PU, United Kingdom
6Department of Biomedical Engineering and Computational Science,
Helsinki University of Technology
, FIN-02015 HUT, Finland
7Harvard Kennedy School,
Harvard University
, Cambridge, Massachusetts 02138, USA
Search for other works by this author on:
a)
Electronic mail: m.beguerisse-diaz08@imperial.ac.uk.
b)
Electronic mail: porterm@maths.ox.ac.uk.
c)
Electronic mail: onnela@hcp.med.harvard.edu.
Chaos 20, 043101 (2010)
Article history
Received:
June 25 2009
Accepted:
July 15 2010
Citation
Mariano Beguerisse Díaz, Mason A. Porter, Jukka-Pekka Onnela; Competition for popularity in bipartite networks. Chaos 1 December 2010; 20 (4): 043101. https://doi.org/10.1063/1.3475411
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Sign in via your Institution
Sign in via your InstitutionPay-Per-View Access
$40.00
Citing articles via
Synthesizing avian dreams
Juan F. Döppler, Melina Atencio, et al.
An integrative dynamical perspective for graph theory and the analysis of complex networks
Gorka Zamora-López, Matthieu Gilson
Data-driven modeling and forecasting of chaotic dynamics on inertial manifolds constructed as spectral submanifolds
Aihui Liu, Joar Axås, et al.