Universal rankings and emerging locality in input-output systems

Assessing the relative influence of constituents in complex organizations is of primary importance in several settings. In complex economies, the input-output framework pioneered by W. Leontief – and the related measures of upstreamness and downstreamness – allows to rank interconnected economic sectors based on their role within supply chains. Among the main practical challenges of the input-output analysis lies the accurate and reliable compilation of input-output matrices using details of the interactions between sectors gathered from surveys.

Interestingly, the input-output analysis in economics also shares similar traits with the classification of how species of an ecosystem interact with each other (according to their so-called trophic levels), or of nodes in a social network (using the PageRank algorithm and the Katz centrality respectively).

In this talk, we will discuss an approximation to calculate the different types of “influence metrics” in the absence of the full knowledge of the interactions between constituents, such as for example the full sector-to-sector interaction matrix. We will show that using only local information about the neighborhoods of nodes is often enough to reliably estimate how influential they are, without the need to infer or reconstruct the whole map of interactions. We also discuss the implications of this emerging locality on the approximate calculation of further non-linear observables (e.g., the network communicability). More in general, our formula allows us to disentangle the effect of the “size” from that of the fine-grained “structure” of interactions in determining the importance of constituents of a complex organization.

Bartolucci, S., Caccioli, F., Caravelli, F., & Vivo, P. (2021). Emerging locality of network influence. [arXiv:2009.06307v4]
Bartolucci, S., Caccioli, F., Caravelli, F., & Vivo, P. (2020). Inversion-free Leontief inverse: statistical regularities in input-output analysis from partial information. [arXiv:2009.06350]