Graph data generating GUI

Need a program that lets me draw graphs (nodes and legs connected to such nodes). Lets me add arbitrary number of nodes and arbitrary number of legs to each node.Allows connected (legs that connect two nodes) and free legs (legs associated with only one node). Allows me to move around the nodes and the legs. Labels each free leg with a unique negative number, labels each positive leg with a unique positive number. Outputs a list of lists of labels of legs for each node. In python.