Should there be a non-recursive option?

I think the documentation needs to be rephrased. I know what you mean with "the node of specified topic" but that is not very clear. Also the term parent is not that good imo. @ros/ros_team What do you think? Any better naming suggestions.

If this is recursive, does it avoid cycles?

I don't have any suggestions for naming. Maybe upstream rather than parent, but upstream implies a tree to me, which again is not necessarily the case.

upstream sounds like a better term to me too.

Get topics to which the node of specified topic subscribes to.

This doc string could be more precise imo, e.g.: "Get topics to which all nodes publishing the passed topic are subscribed to."

When thinking about this more the logic to consider upstream topics (recursively or non-recursively) could be useful beyond rostopic hz. Maybe it would be better to have a separate verb (or an existing one with special arguments) which returns that upstream topic list. And then the result of that can be passed to rostopic hz?

Anyway before integrating this feature a bug with multiple topics and rostopic hz needs to be addressed: #712 (comment)

upstream sounds like a better term to me too.

Get topics to which the node of specified topic subscribes to.
This doc string could be more precise imo, e.g.: "Get topics to which all nodes publishing the passed topic are subscribed to."

I agree.

When thinking about this more the logic to consider upstream topics (recursively or non-recursively) could be useful beyond rostopic hz. Maybe it would be better to have a separate verb (or an existing one with special arguments) which returns that upstream topic list. And then the result of that can be passed to rostopic hz?

+1
Maybe rostopic upstream /topic?

The proposed verb name upstream sounds ok to me. @ros/ros_team Any thoughts on this?

Fine by me.

Closing due to long time of inactivity. Please consider opening a new PR targeting the current default branch if you are still interested in getting this patch merged.