# A Small-World Network Tames Financial Statement Complexity and Opens a Shortcut to Financial Education

Posted: 26 Jul 2018 Last revised: 14 Nov 2023

See all articles by Alfredo Lacayo Evertsz

## Alfredo Lacayo Evertsz

Florida International University - College of Business; Qbit Solutions Research Team

## Lizelia Bravo Boza

Qbit Solutions Research Team

Date Written: June 16, 2018

### Abstract

Double-entries are the fundamental building blocks of the financial statement information of any business. Financial statements can be described by complexity theory because they emerge from the microscopic interactions (Johnson, 2011, Loc. 185) of double-entries. Double-entries are also consistent with complexity theory because they are made up by a set of nodes, the accounts, which are connected by a link. The link is the flow of wealth that connects the accounts and forms the double-entry. In this paper, we show how the infinite number of probable double-entries, can be condensed down to a bare-minimum in a finite bound that is referred to as a small-world network.

How is this possible? To go from double-entry infinity to the small-world network, we condense all accounts (nodes) that share a common essence into a cluster of nodes. For instance, all debt due within twelve months is condensed into the cluster: short-term liabilities. This is done for all conceivably possible accounts until a finite layer of 12 clusters is built. We then condense the 12 clusters into 4 superclusters, which are Sales, Expenses, Assets and Funds. The final step is to condense all links from the microscopic level, into just 12 short-path links that connect the 4 highly-clustered nodes at the macroscopic level (Watts & Strogatz, 1998), see fig. 1. This relatively simple network contains double-entry infinity and thus, the entirety of Luca Pacioli’s double-entry system because it has the essential combinatorial elements to recreate any relevant double-entry.

What is the benefit of this? The benefit is twofold. First, the proposed small-world network gives us a bird’s-eye view of how wealth flows through a business, which maps the fundamental framework for financial management. Additionally, this leads us to a complexity-based algorithm, AKA computational network (Hexmoor, 2015), because we can use the network as a search space, or computational resource to process financial statement information in an ultra-fast way. The processing of financial statement information implies following a set of computable steps to convert raw double-entry information in word problems (e.g., “an owner’s contribution” a “credit sale of an inventory item” or “obtaining a bank loan,” etc.), into useful financial statement information and thus completing the algorithmic cycle from problem to solution.

The boost in processing speed occurs because the condensation of double-entry infinity into a small-world network encodes all answers behind just 12 doors to find the solution to any relevant problem. Contrary to this simplicity, the traditional map from 1494 is extremely complex, which makes it much more difficult to find the answers. Since ultra-fast processing of financial statements implies ultra-fast financial literacy for people following the steps to solve the problems, the new algorithm dramatically shortcuts the time and the effort to understand financial statements. Results are based on solid empirical data.

The presented algorithm is called Financial Qbits and its fully-visual/small-world network approach has successfully trained people in record time at three US Universities: Florida International University, Florida Atlantic University and the University of Rhode Island. Financial Qbits is one more example of the universality and usefulness of complex networks theory, as networks are indeed everywhere and we can use our understanding of their properties for the benefit of society.

Keywords: small-world network, complexity theory, phase transition diagram, double-entry information, financial education, financial accounting

Suggested Citation

Lacayo Evertsz, Alfredo and Bravo Boza, Lizelia, A Small-World Network Tames Financial Statement Complexity and Opens a Shortcut to Financial Education (June 16, 2018). Available at SSRN: https://ssrn.com/abstract=3197660 or http://dx.doi.org/10.2139/ssrn.3197660

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