How to contact author whose work I built off of?
It's appropriate to contact the authors, particularly if they are still active researchers. Before sending them the manuscript or telling the entire story, perhaps ask if they would be willing to keep your results confidential until publication.

As far as formal permission to reproduce their graph, it's very likely that the authors don't hold the copyright. Most authors sign over copyright to the publisher, so you may have to query them. Even so, it would be polite and advisable to notify the authors that you are planning to reproduce a piece of their work for comparison.