Whether you hide or display the old graph, neither method really helps the user visualise the change. Either way, you present the new graph abruptly leaving the user to work out what changed, if anything.
Ideally you should be indicating not that there is a change going on, but also what that change is relative to what was there before.
To help the user transition, you should make the data itself communicate the transition. That can be done in three steps:
Indicate the areas of change: Animate the graph from the old version to the new version. Users can see the fastest moving parts as the points of most change.
Retain what the change is relative to: Keep a copy of the old graph as a background, but faded, so that the user can see the relative difference between old and new.
On completion, lose the old data: Once the animation is complete and the new version is shown, transition a fade out of the old background graph so that it disappears leaving only the new graph.
Ideally, there would also be an undo/redo, where the transitioning works in reverse, and forward again, so the user can review if they wish.
I appreciate that's probably more work than you anticipated!