Link 1: http://i.imgur.com/bpRCfjq.jpg
Link 2: Euler Circuit: http://i.imgur.com/PW7j5q3.jpg
Okay the Euler circuit is pretty simple i think. I will update my answer later when i can upload it.
Each vertex has an even degree. and there are multiple ways to draw the circuit. But as along as i used every edge at least once AND ONLY ONCE (even though i touched vertices MULTIPLE times) It is a Euler circuit.
So is this correct? -