Basically, Google is enabling you to keep your readers on your site by giving you recommended links to your site for free.
The issue at hand (and to answer your question) is that this mouseover menu doesn't add value. It moves attention to popular content - not must read content. Google claims to know what the next page should be, I claim to already have that functionality. And it doesn't involve likes, votes, +1s, keywords, tags or ranks - it's about original and relevant content.
In your specific case, it sounds like you want users to look at content that you pick as relevant. In most cases that Google is targeting, they want to give authors the ability to have their readers pick what to read based on social signals and past reading/+1 behavior.