In a graph with nodes, the longest simple path (no repeated nodes) has edges. You cannot have a simple path with or more edges without repeating a node, which creates a cycle. After round , you have shortest paths with edge. After round , shortest paths with edges.
After round , shortest paths with edges. After rounds, you have checked all possible simple paths. If no negative cycle exists, distances stop changing because you have found the true shortest paths. If distances still change, a negative cycle exists.