Competition for Popularity in Bipartite Networks

Abstract

We present a dynamical model for rewiring and attachment in bipartite networks in which edges are added 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 very large set of options.

13 Pages, 19 Figures

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• Structure and tie strengths in mobile communication networks
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• The clustering coefficient and community structure of bipartite networks
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• Latent geometry of bipartite networks
• The reinforcing influence of recommendations on global diversification
• HellRank: A Hellinger-based Centrality Measure for Bipartite Social Networks
• Opinion dynamics on tie-decay networks