Competition for Popularity in Bipartite Networks

TL;DR

This paper introduces a dynamical model for bipartite networks inspired by Netflix data, capturing how users and videos acquire ratings over time, revealing power-law distributions and activity bursts, with implications for systems involving large choice sets.

Contribution

The paper develops a new dynamical model for bipartite networks that accurately reproduces observed rating distributions and activity patterns in Netflix data, linking empirical findings with theoretical modeling.

Findings

Rating distributions follow power laws with exponential cutoffs.

User activity exhibits bursty behavior with long inactivity periods.

Model predictions align well with Netflix data.

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.