*Reference: ***Euler Circuit**
Where an

Euler circuit must pass each

link (

edge) exactly once, a Hamiltonian circuit pass go through each

node (

vertex) exactly once. Side note, I learned this week, it's pronounced 'Oil-er', like one who oils, and not 'Euler' like ruler. Please don't sound as ignorant as I did in front of your discrete math professor.

*Reference: ***Hamiltonian Path**
While a Hamiltonian path must pass each node exactly once, a Hamiltonian circuit must pass each node exactly once,

**and end at the node the path started at**. This said,

All Circuits are Paths.

*Reference: ***Traveling Salesman Problem**
Commonly referred to as a

TSP, it simulates a salesman who must visit each node preferably once, go home at the end of the day, and have traveled the least distance needed. Any path the salesman takes is a Hamiltonian Circuit.