Question: I am currently studying Graph Theory and want to know the difference in between Path , Cycle and Circuit. 

I know the difference between Path and the cycle but What is the Circuit actually mean.

Answer: 
All of these are sequences of vertices and edges. They have the following properties : 

1. **Walk**    : Vertices may repeat. Edges may repeat (Closed or Open)
2. **Trail**     : Vertices may repeat. Edges cannot repeat (Open)
3. **Circuit** : Vertices may repeat. Edges cannot repeat (Closed)
4. **Path**     : Vertices cannot repeat. Edges cannot repeat (Open)
5. **Cycle**    : Vertices cannot repeat. Edges cannot repeat (Closed)

**NOTE** : For closed sequences start and end vertices are the only ones that can repeat.
In a circuit we have can repeated vertices, but we cannot in a cycle.