d[e.b] = max(-INF, d[e.a] + e.cost);

The above implementation looks for a negative cycle reachable from some starting vertex $v$; however, the algorithm can be modified to justlooking for any negative cycle in the graph. For this we need to put all the distance $d[i]$ to zero and not infinity — as if we are looking for the shortest path from all vertices simultaneously; the validity of the detection of a negative cycle is not affected.

The above implementation looks for a negative cycle reachable from some starting vertex $v$; however, the algorithm can be modified to justlook for any negative cycle in the graph. For this we need to put all the distance $d[i]$ to zero and not infinity — as if we are looking for the shortest path from all vertices simultaneously; the validity of the detection of a negative cycle is not affected.

For more on this topic — see separate article,[Finding a negative cycle in the graph](finding-negative-cycle-in-graph.md).