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Summary
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Directed multilayer networks exhibit both link alignment (multiplexity) and anti-alignment (multireciprocity). Multireciprocity, where links in one layer are reciprocated by opposite links in another, is a key finding in the world trade network.

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Area of Science:

  • Network Science
  • Complex Systems
  • International Trade Analysis

Background:

  • Real-world multilayer networks display complex dependencies between layers.
  • Directed links introduce two types of dependencies: multiplexity (alignment) and multireciprocity (anti-alignment).

Purpose of the Study:

  • To introduce and quantify multireciprocity in directed multilayer networks.
  • To analyze the interplay of multiplexity and multireciprocity in the World Trade Multiplex (WTM).

Main Methods:

  • Development of multiplexity and multireciprocity matrices for binary and weighted networks.
  • Statistical validation against maximum-entropy null models to account for node heterogeneity.
  • Empirical analysis of the World Trade Multiplex (WTM) dataset.

Main Results:

  • The WTM exhibits significant multiplexity and multireciprocity, largely explained by node degree/strength.
  • Residual multireciprocity allows classification of commodity trading patterns (same/opposite directions).
  • WTM multireciprocity is lower than aggregate network reciprocity; reciprocity is group-based for commodities.

Conclusions:

  • Multireciprocity is a crucial factor in understanding directed multilayer networks, particularly in trade.
  • Findings inform international trade research on product spaces and economic complexity.
  • Reciprocity in trade networks is more inherent to related commodity groups than individual commodities.