I'm trying to convert an instance of zero subset sum to zero weight cycle in directed graphs to prove that the ZWC problem belongs to the np-complete class. My solution: for each element like x in the zero subset-sum array, create a node in graph G and add an edge from this node to all the other nodes in the graph with weight x. Then if this graph contains a zero weight cycle, our zero subset sum has a solution and vice versa. But when I searched for the solution on the web I found a different way of constructing the graph.
Now the question is that are there any problems with my reduction algorithm?