I would focus on creating the classes for the Nodes and Edges first. For instance the Node class needs to know its own position, an Edge would have 2 Node fields (for the start and the end) and a weighting (might be distance between start and end nodes).
Both the Node class and Edge class would have their own method to draw itself e.g. display()
Once you have the classes then create a small fixed network of nodes and edges and make sure they render OK
Then you can consider how to create the network dynamically with the mouse.
Finally create the path finding algorithm and test it.