The triangular structure beyond pairwise interactions affects the robustness of the world trade networks.

Unlike hollow triangles formed through pairwise interactions, a filled triangle or two-simplex comprises three nodes that form a group and represent the most fundamental higher-order interaction. To analyze the effects of higher-order triangles on the robustness of world trade networks, we integrate multilateral regional trade agreements and import-export world trade data to construct two-simplex higher-order trade networks. The topological characteristics indicate a significant growth in the scale and complexity of trade networks over time, with a notable decline in 2020. Then, we introduce node attack strategies designed to simulate scenarios where the key countries or regions withdraw from the trade network. It is revealed that network robustness has improved along with size and complexity, although it diminished in 2020. To further explore the factors influencing the changes in network robustness, we generate higher-order synthetic trade networks based on the random simplicial complex (RSC) model and the scale-free simplicial complex (SFSC) model. The synthetic trade networks demonstrate that increasing the average degree enhances robustness, while merely increasing the number of nodes or filled triangles can weaken it. Additionally, scale-free higher-order networks exhibit lower robustness due to vulnerability of the hub nodes, in contrast to the higher resilience of random simplicial complexes. These insights emphasize the importance of fostering multilateral interactions and strengthening ties for network robustness.