Hello I can help you with this project I have solid knowledge of Qt, as I'm working on it since version 4.6. Also I'm a senior C++ programmer so I can offer valued help for you.
I'm not expert in the graph part but as each module is easy to integrate because is a consistent api it shouldn't be a problem. Also I know very well the DFS algorithm so I believe this project is perfect for me.
Please contact me to discuss the project.