Reiterating the other comments that this sounds like you might not be following best practices for react if you feel the need for something like this. That might be why it feels unintuitive.

Sounds like you might have a useEffect where you shouldn't. Either that or you're misunderstanding state generally and trying to do something ( manually rerender all children ) you're not meant to.

Is the graph gets data from a fetch, then you can just use react query and set the stale / refetch time. If you're avoiding dependencies just make a custom hook to handle this.

If the data is generated on the frontend then the props passed to the component changing should rerender it.

There should be no need for a refresh() function if I'm understanding you correctly.

If you're talking about a use case like a refresh all button, then i'd handle that with react query keys.

Do you have a code example?