Does anyone know if you can force (or perhaps even coax!) the activity stream to appear?
The choice of what appears down the right hand side (activity feed, suggested people, suggested groups, etc) seems to change a little randomly, but I can't figure out why that happens or how to force certain elements to be displayed.
In my experience in my network, the activity stream only appears on the "home" screen and it shows what people have recently looked at and what files they've downloaded and who's joined a group you're a part of. Anyway, to my knowledge, there's no way to interact with that stream as an admin and force it to do anything. The suggested people and groups changes randomly - all determined by your activity the graph shows you things that it thinks may be of interest to you.
The somewhat infuriating thing to me is that the second user suggested is ALWAYS a pending user. And that account is often one that is probably not supposed to be in your network. Could be a wrong email address, wrong spelling of a name that someone had in their contacts and the Yammer app grabbed, a former employee (again, because the email was grabbed likely from someone's mobile phone contacts). The only way I know to resolve that is to do a semi-regular check of the pending user list against your active directory and then purge and block the non-member accounts from the Yammer pending user list. That can be somewhat impossible in large organizations, but for small Yammer networks, it's pretty helpful.
Further details on how to delete those annoying pending accounts that Amy mentioned is available here.
Benjamin, there's an undocumented API which allows you to at least look at the activity feed programmatically. I suppose you could write an app (or a Flow!) to call that API regularly and post the results to SharePoint or whatever and then run further data analysis against that repository. Not exactly interact, but gives you a visual into what's happening there.