Road map network Nodes marking GIS

This is a Road network map of Karachi
Where our main location is bahria town and other locations are universities of whole Karachi where total universities are 30.
As you can see I have made longest route and shortest route as well from bahria town to each University.
Now What I need is
1. Put nodes as a point shape file on both roads longest and shortest. As you know two connecting points or two intersecting points of A road is called node. If we are working on longest road then any 2 roads in longest road that is connecting 1 point with each other will be called as node. Nodes will be labelled as N1 and N2 N 3 and so on.
2. In nodes we will count edges any curve between Node 1 to node 2 is called as edge.