The Bellman$-$Ford algorithm is a classic algorithm used to find the shortest paths from a single source vertex to all other vertices in a weighted graph, even in the presence of negative weight edges $($as long as there are no negative weight cycles reachable from the source vertex$).$ Its time complexity is O$($V $*$ E$),$ where V is the number of vertices and E is the number of edges in the graph. It's less efficient compared to Dijkstra's algorithm for finding shortest paths in graphs with non$-$negative edge weights, but it can handle graphs with negative weight edges.