Graph Reputation does not graph the reputation of someone, that would be silly (way too obvious). Instead it updates the column of reputation points earned numbers on the right of the graph, and it changes the highlighted area on the graph.
If you use the mouse to click and highlight a time period, the button will do absolutely nothing. But if you manually enter the dates below the graph, the button will update the highlighted area and the points (a twofer, if you will)!...... (although, simply changing the focus away from the date entry text boxes will also achieve the same effect, fwiw...)