How will I determine fundamental loop equations from a graph which contains 3 and 2 terminal circuit elements?
You can still do regular loops. For example: V65 + V54 + V48 + V86 = 0, where the indices refer to your nodes as marked in the picture.

So we have 1V + V54 + 0.5V - 2V = 0, V54 = 2V - 1V - 0.5V = 0.5V. 

You can calculate the other element voltages across the terminal of the transistors the same way.