[DSRP Evidence](https://dsrpevidence.org/)

# More Links but Fewer Effective Routes: Entropy and Resilience in Global Lithium, Cobalt and Nickel Trade Networks

Liu et al., 2026, Entropy — Network Science

Patterns: [Systems](https://dsrpevidence.org/pattern/systems), [Relationships](https://dsrpevidence.org/pattern/relationships)

## In short

The network's whole-level functional property (route diversity, resilience) does not scale with the simple count of its parts (links), and entropy is used as a relational bridge connecting network structure to resilience outcome.

## What they found (results)

Analyzing value-weighted global trade networks for lithium, cobalt and nickel (2010-2024), the authors found the number of trade links rose (e.g., lithium links from 180 to 290) while the entropy-effective number of functional routes fell sharply (from 38.68 to 12.75), and flow entropy correlated with a network's resilience to targeted attack (rho=0.754, p=0.001).

## Abstract

Counts of trade links are often used as evidence of diversification, yet they say little about how value is distributed across those links. Using bilateral flows for selected lithium, cobalt and nickel products among 72 economies from 2010 to 2024, we built directed, value-weighted networks and examined them with multiscale entropy measures, lagged formation models and disruption tests. Here, entropy is used in the information-theoretic sense to measure how evenly trade value, network weight or motif participation is distributed across routes and structural modes; for route-value entropy, exp(H) is the effective number of equally weighted routes. The number of lithium links increased from 180 to 290, but its entropy-effective route count declined from 38.68 to 12.75. Nickel displayed a similar divergence, falling from 118.84 to 21.81 effective routes as links increased, whereas cobalt moved in the opposite direction. Across layer-years, flow entropy was associated with the share of trade retained under targeted attack (ρ = 0.754; Holm-adjusted p = 0.001). Binary dependence between lithium and nickel rose over time, although their weighted divergence was still 0.907 in 2024. In the China-removal experiment at the largest capacity margin, 95.7% of nodes survived but only 33.8% of trade value remained. For these product baskets, a larger network therefore need not be a more diversified one, and preserved connectivity can coexist with substantial economic loss.

These researchers were not testing DSRP. The finding is theirs; the correspondence to DSRP is drawn by this site.

[Source](https://doi.org/10.3390/e28080913)