Universal rankings in complex input-output organizations

Por • 17 sep, 2020 • Sección: Economía

Silvia Bartolucci, Fabio Caccioli, Francesco Caravelli, Pierpaolo Vivo

The input-output balance equation is used to define rankings of constituents in the most diverse complex organizations: the very same tool that helps classify how species of an ecosystems or sectors of an economy interact with each other is useful to determine what sites of the World Wide Web — or which nodes in a social network — are the most influential. The basic principle is that constituents of a complex organization can produce outputs whose «volume» should precisely match the sum of external demand plus inputs absorbed by other constituents to function. The solution typically requires a case-by-case inversion of large matrices, which provides little to no insight on the structural features responsible for the hierarchical organization of resources. Here we show that — under very general conditions — the solution of the input-output balance equation for open systems can be described by a universal master curve, which is characterized analytically in terms of simple «mass defect» parameters — for instance, the fraction of resources wasted by each species of an ecosystem into the external environment. Our result follows from a stochastic formulation of the interaction matrix between constituents: using the replica method from the physics of disordered systems, the average (or typical) value of the rankings of a generic hierarchy can be computed, whose leading order is shown to be largely independent of the precise details of the system under scrutiny. We test our predictions on systems as diverse as the WWW PageRank, trophic levels of generative models of ecosystems, input-output tables of large economies, and centrality measures of Facebook pages.

arXiv:2009.06307v1 [physics.soc-ph]

Physics and Society (physics.soc-ph); Statistical Mechanics (cond-mat.stat-mech)

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