The Dynamics of Interactions in the Structure of Currency Denominations Using the Horton-Strahler Methodology

Abstract

This paper examines the structure of currency denominations and its impact on transactional efficiency. The main objective is to assess the compatibility between the effective supply of coins and banknotes and the optimal demand of economic agents, while accounting for microeconomic constraints. We develop an innovative methodology by adapting the Horton-Strahler topological framework, originally designed for hydrological networks, to monetary circulation. Two key parameters are considered: monetary amplitude ( K ), reflecting the overall intensity of circulation, and spectrum width ( L ), measuring the range of denominations available. Empirical estimation combines normalized distribution modeling (Hentsch’s law), least-squares fitting, and binary tree simulations using data from the BCEAO 1 , commercial banks, and field surveys in Côte d’Ivoire (2010-2019). The results show that L grows proportionally with GDP 2 , while K increases more slowly, preserving the stability of the ratio N = K / L . Simulations reveal that balanced structures centered on intermediate denominations (100 - 1000 FCFA 3 ) enhance monetary resilience and minimize transactional bottlenecks, whereas extreme-dominated distributions (very small or very large denominations) slow convergence and destabilize circulation. These findings confirm the critical role of denomination structures in shaping economic efficiency.