Fundamental Products and Autonomous Sets: An Algorithmic Approach

The main goal of this paper is to analyze an economy through its symmetric input-output table by using Graph Theory. After providing a definition of the characteristic digraph for the economy, the authors give some properties and algorithms to characterize and compute the fundamental products and, later, the autonomous sets of the studied economy. Six of these algorithms are explained in detail and formulated; the best choices are also implemented with the computational package Mathematica, compared in terms of efficiency, and applied to real input-output matrices from G reece.