Is an element that is returning to itself Transitive?

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Lets say you have a graph and x goes to y, y goes to itself and then y goes back to x. Can you call this a transitive relation?

My answer: yes it is transitive because x R y, y R y and y R x but what confuses me is that I learned transitivity as follows:

if x R y and y R z then x R z. But in the case above x R x if you reason like this. If find this a bit confusing. Can anyone please explain this?

Thanks in advance