I am trying to make a few interactive graph visualisations in my Django web application using Python. I found Graphviz and was able to output a static graph (as a .png image) on
It seems like an approach that fits what you are trying to do might be to use svg in the browser an/or javascript. I think most of the modern browsers support SVG and would allow you to do some pretty cool interactive graphs. The server could provide a json feed of the datapoints needed to render the graph. I don't know off hand the tools that are available, but I've seen some pretty cool graph demos constructed without flash through client-side approaches.
As an alternative, you could pre-render a bunch of graph images that the user would likely view and then just fetch those as the user interacts with the graph. This might work if the graphs don't change that frequently and if the number of alterations that the user would make is small, but you'd have to re-render every time the graph changes.