二分网络中的人气竞争
Competition for Popularity in Bipartite Networks
摘要：
我们提出了一个动力学模型重新布线和附件的二分网络中，边缘之间添加的节点属于目录，可以是固定的大小或增长的大小。该模型的动机是对视频租赁服务Netflix的数据进行实证研究，Netflix邀请其用户对其目录中的视频进行评级。我们发现，由用户给出的评级数量的分布和视频收到的评级数量都遵循指数截止的幂律。我们还研究了Netflix用户的活动模式，发现在长时间不活动之后会出现强烈的视频评级活动。我们推导出常微分方程模型的收购边的节点随着时间的推移，并获得相应的时间依赖的度分布。然后，我们将我们的结果与Netflix的数据进行了比较，发现两者吻合得很好。最后，我们讨论了如何目录模型可以用来研究系统中，代理人被迫选择，率，或优先考虑他们的相互作用，从一个非常大的选项。
英文摘要：
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.
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