# Temporal rich-club phenomenon and its formation mechanisms in international trade: Evidence from new energy minerals

## TL;DR

This paper studies how key countries in global trade of new energy minerals form a stable group over time and identifies the factors behind this pattern.

## Contribution

A new analytical framework using the DII method to uncover the mechanisms driving the formation of temporal rich-club structures in trade networks.

## Key findings

- Trade networks of new energy minerals show statistically significant temporal rich-club characteristics.
- Three coexisting mechanisms—path dependence, homophily, and national attributes—drive TRC formation.
- The DII method effectively identifies key drivers of TRC evolution in time-varying networks.

## Abstract

The temporal rich-club (TRC) phenomenon, in which a tight and persistent collection of key nodes is formed, is widely observed in real-world settings. However, the underlying mechanisms that drive the formation of TRC structures remain insufficiently understood. This study investigates the TRC phenomenon in international trade through an analysis of 30 time-evolving trade networks of new energy minerals (cobalt, lithium, nickel, and copper) from 1994 to 2023. We select and weight the features in network evolution using the differentiable information imbalance (DII) method and develop an analytical framework to analyze TRC formation and elucidate its evolutionary mechanism. The empirical results demonstrate statistically significant TRC characteristics in these trade networks. Mathematical modeling reveals that TRC emergence is driven by three coexisting mechanisms, including path dependence, degree of homophily, and intrinsic national attributes such as economic development and resource endowment. These findings provide additional insights into the stability and evolution of global energy mineral trade networks.

•Analysis of new energy mineral trade network evolution from 1994 to 2023•Incorporating 11 node-level trade attributes•A scalable DII feature-selection framework for uncovering TRC mechanisms•Identifying joint drivers of TRC formation

Analysis of new energy mineral trade network evolution from 1994 to 2023

Incorporating 11 node-level trade attributes

A scalable DII feature-selection framework for uncovering TRC mechanisms

Identifying joint drivers of TRC formation

Earth sciences; Energy resources; Network modeling; Energy materials