Online videos have shown tremendous increase in Internet traffic. Most video hosting sites implement recommender systems, which connect the videos into a directed network and conceptually act as a source of pathways for users to navigate. At present, little is known about how human attention is allocated over such large-scale networks, and about the impacts of the recommender systems. In this paper, we first construct the Vevo network -- a YouTube video network with 60,740 music videos interconnected by the recommendation links, and we collect their associated viewing dynamics. This results in a total of 310 million views every day over a period of 9 weeks. Next, we present large-scale measurements that connect the structure of the recommendation network and the video attention dynamics. We use the bow-tie structure to characterize the Vevo network and we find that its core component (23.1% of the videos), which occupies most of the attention (82.6% of the views), is made out of videos that are mainly recommended among themselves. This is indicative of the links between video recommendation and the inequality of attention allocation. Finally, we address the task of estimating the attention flow in the video recommendation network. We propose a model that accounts for the network effects for predicting video popularity, and we show it consistently outperforms the baselines. This model also identifies a group of artists gaining attention because of the recommendation network. Altogether, our observations and our models provide a new set of tools to better understand the impacts of recommender systems on collective social attention.