Summary: It is well-known that in a directed graph, if deleting any edge will not affect the shortest distance between two specific vertices \(s\) and \(t\), then there are two edge-disjoint paths from \(s\) to \(t\) and both of them are shortest paths. In this article, we generalize this to shortest \(k\) edge-disjoint \(s\)-\(t\) paths for any positive integer \(k\).