Look at the Status Bar. It show the Active Person when in the People view. When you Filter or Searchbar for a person who does not match, the Active Person can be hidden from the Viewable records. The search does NOT change the focus of the view.
I do not have all the GraphView components installed to do tests with its search. But I seem to recall that it changed the focal person of the Chart.
Such an option doesn’t exist yet and would mean a pretty significant change to workflows (and documentation). And having it independent of the Sidebar creates a lot of complexity for users about the interaction of the Filter gramplet and the Searchbar. That is not a deal-breaker… but it needs discussion. Possibly a the “GEPS” level discussion.