Before revision: A graph representation of the financial relations in a given monetary structure is proposed. It is argued that the graph of debt-liability relations is URLanized and simplified into a tree structure, around banks and a central bank. Indeed, this optimal graph allows to perform payments very easily as it amounts to the suppression of loops introduced by pending payments. Using this language of graphs to analyze the monetary system, we first examine the systems based on commodity money and show their incompatibility with credit.
After revision: The nature of monetary arrangements is often discussed without any reference to its detailed construction. We present a graph representation which allows for a clear understanding of modern monetary systems. First, we show that systems based on commodity money and show their incompatibility with credit.