Competition for Popularity in Bipartite Networks

One of my papers was published in Chaos yesterday. You can find a link to it here. It uses data from the Netflix competition, and it concerns the human dynamics of video rentals.

Title: Competition for Popularity in Bipartite Networks

Authors: Mariano Beguerisse Díaz, Mason A. Porter, and Jukka-Pekka Onnela

Abstract: 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.