TITLE: What is difference between cycle, path and circuit in Graph Theory
QUESTION [48 upvotes]: 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.

REPLY [98 votes]: All of these are sequences of vertices and edges. They have the following properties : 

Walk    : Vertices may repeat. Edges may repeat (Closed or Open)
Trail     : Vertices may repeat. Edges cannot repeat (Open)
Circuit : Vertices may repeat. Edges cannot repeat (Closed)
Path     : Vertices cannot repeat. Edges cannot repeat (Open)
Cycle    : Vertices cannot repeat. Edges cannot repeat (Closed)

NOTE : For closed sequences start and end vertices are the only ones that can repeat.