Owing Graph Minimization

I&#x27;m confused. The article seems to require that people pay whoever they owe, as opposed to whoever is owed money. It seems we can simply sort the people by the amount owed, then have the person at the top of that list pay the person at the bottom, and repeat until all debt is resolved. This is an nlog(n) algorithm (for the sorting), and creates at most n edges (since, for every transaction, someone either pays back everything they owe, or someone gets paid everything they are owed).<p>Is there something I&#x27;m missing?

The output list makes the tuples different than the input... there is no way that john suddenly owes beryl 25 for example.<p>I don&#x27;t see an explanation for this in the text - but a directed edge seems to switch from a semantic of &quot;owes&quot; to &quot;is owed&quot;.

Another way to think of this problem is find a feasible flow in a complete graph that satisfy all vertex demands and using minimum number of edges.