I'm little confused by computing a time complexity for
Dijkstra algorithm. It is said that the complexity is in $O(|V|^2)$ - Wikipedia - Dijkstra, which I understand. It's because for each node, we could theoretically relax edges going to each vertex so it is $n * n$ times, respectively $n(n-1)$.
On the other hand, I can't figure out why this complexity isn't $O(|E|+|V|)$. For each $v \in V$, we relax only those edges $e$, which weren't computed yet. If vertex $v$ is already computed (red on gif above), we don't need to work with it anymore.
So can I say that in one way, it is true that
Dijkstra is in $O(|V|)$, but if we can put into the computation number of edges, I can say that it is in $O(|V|+|E|)$?