I read about Djikstra’s algorithm and I want to be sure about two fundamental things, would appreciate if you could answer me mathematically so I can understand how words are translated to math so I can use it in other uses as well.

so here are my questions:

- if we mark the shortest path Djikstra’s algorithm found in some network with $ n$ stations in some topological construction: does it necessarily find the shortest path between each pair of vertices?
- assume there’s at least an additional path, somewhere from $ s$ to $ t$ , with same weight but with different edges (meaning both paths don’t have a common edge), how can we find this edge?

I don’t understand it well and I will really appreciate explanation so I can understand it better.

Watched videos, read materials online, and tried to concise what I am not sure about so I can request it here to deepen my understanding.

thank you for your time and assistance