This study by Pew Research Center does not analyze the algorithm itself, but derives insights from what is actually shown to users, and the results are interesting. In short: YouTube recommends slightly longer, and progressively more popular (higher view count) videos in relation to the one you started with. And only (depending on age) 15-25% of users say they don't use the recommendation feature - while roughly 2/3 of users in all age brackets use recommended videos occasionally. Also, there's a short tail of recommendations: During >170,000 random five-step walks through YouTube, 72% of recommended videos in this analysis were only shown one time, and 26% of videos were shown 2-10 times, but 2 percent of videos were shown 11-100 times and a tiny number of videos (<1%) were shown over 100 times as recommendations.
More super-interesting findings (51% of >4500 surveyed YouTube users say they go there to learn how to do stuff they haven't done before) and stats here: