Need advices for building simulator for algorithms on Graph

[Long Ph. Le]

I want to simulate the way that a vaccum cleaner robot cleaning on an unknown room. The room will be presented as a 2D grid graph and i will use different algorithms to planning and finding the "solution" for the robot to clean the room as much as possible. So I want to try this with C++ and Qt for building an cross platform application. I just learned basic Model/View and signal/slot concepts in Qt but still dont have any experience in developing Qt application before. I target my app to simulate on a large graph (about 10000 nodes) so the optimization on render and design structure is neccessary. My approach is i will present the map in GraphicsView, each Node will be a GraphicsItem, but how can i seperate the Model and View in this situation? Does i need to create a GraphModel inherited from QAbstractItemModel to manage and control Nodes in the graph? Or can anyone give me some advices for better approach? I just learned about Qt for about 2 weeks and still be new, if u guys can, please explain ke I'm 5.