Is there a way to pass many arguments and not have an ugly url?
You could use form submission or cookies to store values, but neither of these are a particularity good ideas. 

I would recommend (if you don't like the URL showing) using AJAX to retrieve/update the graph. You still have the ugly url but you hide it inside the ajax request. 

So your module displays

/mypath

but the request could be

/mymodule/displaygraph/x/as/32432/s///