window.opener will return a reference to the window object of the window that opened it.
In the first window, you can leave a global reference (let's say var graphThing or window.graphThing) to whatever object you need to manipulate. Then, the window that's launched from the original window can call window.opener.graphThing to access the first window's graphThing.
To access a property of the child window (let's say global var childGraphThing or window.childGraphThing) from the parent that opened it, you can keep a reference to the child window by opening it like this:
var childWindow = window.open('childGraph.html', 'blank_');
Then, you can access it's properties like this:
var childWindowGraphThing = childWindow.childGraphThing;