I have a weighted graph where each edge is a 1d vector eg if weight going from A to B is 1 then from B to A it is -1. In the graph each cycle should add to zero though sometimes the weights have errors and in that case a cycle will not add to zero.
So for example if the weight from A to B is 1 and B to C is 1 then for the cycle to sum to zero C to A must be -2 and there is an error if it is anything else. Please note that in general the cycles can involve an arbitrary amount of nodes.
What is the best algorithm for detecting these errors? IE what is the best algorithm for finding all weights that have errors and so are causing the cycles to add to a non zero value?