Accounting

Open Risk White Paper 19: Connecting the Dots: Accounting Graphs for Double and Quadruple-Entry Bookkeeping

We develop the concept of an accounting graph as an intuitive and flexible tool that can faithfully represent widely used accounting concepts. More specifically, a weighted directed multigraph representation is applied to model standard double-entry bookkeeping (DEB) of individual accounting entities but extended to also provide a consistent accounting graph for larger economic networks that feature multiple transacting entities (so-called quadruple-entry accounting). We illustrate the concepts with stylized accounting examples. Such accounting graphs are promising both as educational tools and towards the application of computational tools on accounting data.

Graphs for Double and Quadruple-entry Accounting

In a new Open Risk white paper we develop the concept of an accounting graph as an intuitive and flexible tool that can faithfully represent widely used accounting concepts. Weighted directed multigraphs representations can model standard double-entry bookkeeping (DEB) of individual accounting entities but can also be extended to to larger economic networks that feature multiple transacting entities (so-called quadruple-entry accounting). Such accounting graphs are promising both as educational tools and towards the application of computational tools on accounting data.

November 11, 2025 (Last Modified: November 12, 2025)

White Papers, Commentary

Reading Time: 7 min.

"The Principles of Book-keeping by Double Entry constitute a theory which is mathematically by no means uninteresting: it is in fact like Euclid's theory of ratios an absolutely perfect one, and it is only its extreme simplicity which prevents it from being as interesting as it would otherwise be. - Arthur Cayley"

qeb_accounting_graph