What is the difference between a Hamiltonian Path and a Hamiltonian Cycle?

Question

The title says it all. I've seen confusing definitions of this, and would appreciate if someone can succinctly clear this up with definitions and examples.

Answer 1

The cycle starts and ends in the same vertex, but the path does not.

Answer 2

Hamiltonian cycle = a cycle (path ending in the same vertex it starts) that visits every vertex ($ n $ edges);
Hamiltonian path= a path that visits every vertex ($ n - 1 $ edges).

In the graph represented by the matrix of adiacence:

01001
10100
01010
00101
10010

We have 1 - 2 - 3 - 4 - 5 or 1 - 5 - 4 - 3 - 2 Hamiltonian paths. Also, 1 - 2 - 3 - 4 - 5 - 1 is a Hamiltonian cycle.

Answer 3

Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once Hamiltonian cycle is a Hamiltonian path that is a cycle, and a cycle is closed trail in which the “first vertex = last vertex” is the only vertex that is repeated.
For more info https://www.whitman.edu/mathematics/cgt_online/book/section05.03.html
https://en.wikipedia.org/wiki/Hamiltonian_path