An Euler circuit (or Eulerian cycle) is an Euler path that starts and ends at the same vertex.
Example: A security guard patrolling every hallway of a building and returning to the starting point.
Every Euler circuit is an Euler path, but not every Euler path is a circuit.
Core distinction:
- Euler path: start and end may differ
- Euler circuit: start and end are the same
If an Euler circuit exists, you can start from any vertex. For an Euler path, you must start from a specific vertex.