Similar to this question, I\'m looking for a way to create a GUI where users are able to see a graph (in the graph theory sense) and interact with it. Vehicl
You might consider the JavaScript library d3. It has some fantastic interactive graph visualisations, and being written in JavaScript it's great for Web UI
I'm uncertain of the live graph building capabilities, but presume simple node and edge addition/removal would be trivial to implement on top of your chosen visualisation type.
Of course, you'd require something like pyjs to interface d3 with your python code, so it might not be suitable.
Regarding nmichaels' answer: having used GraphViz extensively, I wouldn't recommend it for your purpose. It generates beautiful static diagrams but is strictly non-interactive.