# Commodity-specific triads in the Dutch inter-industry production network

## TL;DR

This paper studies triadic patterns in the Dutch production network to understand how economic shocks might spread, focusing on individual commodities.

## Contribution

The study introduces null models to analyze triadic motifs in commodity-specific production networks and identifies a 'triadic fingerprint' for each commodity.

## Key findings

- Most single-product layers in the network have no significant triadic motifs or only two or fewer.
- A 'triadic fingerprint' can be used to reconstruct product-specific networks using pairwise interactions.
- The results help identify fine-grained economic structures useful for policymakers.

## Abstract

Triadic motifs are the smallest building blocks of higher-order interactions in complex networks and can be detected as over-occurrences with respect to null models with only pair-wise interactions. Recently, the motif structure of production networks has attracted attention in light of its possible role in the propagation of economic shocks. However, its characterization at the level of individual commodities is still poorly understood. Here we analyze both binary and weighted triadic motifs in the Dutch inter-industry production network disaggregated at the level of 187 commodity groups, which Statistics Netherlands reconstructed from National Accounts registers, surveys and known empirical data. We introduce appropriate null models that filter out node heterogeneity and the strong effects of link reciprocity and find that, while the aggregate network that overlays all products is characterized by a multitude of triadic motifs, most single-product layers feature no significant motif, and roughly 85% of the layers feature only two motifs or less. This result paves the way for identifying a simple ‘triadic fingerprint’ of each commodity and for reconstructing most product-specific networks from partial information in a pairwise fashion by controlling for their reciprocity structure. We discuss how these results can help statistical bureaus identify fine-grained information in structural analyses of interest for policymakers.