Algorithm to simplify a weighted directed graph of debts

Question

I\'ve been using a little python script I wrote to manage debt amongst my roommates. It works, but there are some missing features, one of which is simplifying unnecessarily

Answer 1

Here is an academic paper which investigates this problem in great detail. There is also some sample code for the different algorithms in Section 8 towards the end.

Verhoeff, T. (2004). Settling multiple debts efficiently : an invitation to computing science. Informatics in Education, 3(1), 105-126.