The Nodal Network

A graph is to be constructed with two types of nodes in it. A and B type. For each of A type node, there must be two B type stations equidistant from each A type node. Initially there is only one node having index 0, where the main node is located. Over a period of time, more and more nodes are extended. There are two functions that can be performed using these nodes(X): Type P: Create a new node