TITLE: distinct edges and vertices (graph theory)
QUESTION [5 upvotes]: I want to ask about the relationship between distinct vertices and distinct edges. 
I was able to come up with an explanation for
"distinct vertices" $\Rightarrow$ "distinct edges".
An edge is considered the same if it has the same endpoints (am I allowed to take this as self-evident?).
Therefore, if all vertices are distinct in a walk, no vertex appears twice, so every edge is distinct.
Is this correct? Also, is the converse true/can I make a counterexample?

REPLY [4 votes]: You are correct, and multigraphs would need a stronger definition.