Network Fragility and Sustainability of a Territorial Yam Supply Chain for Food Security in the Colombian Caribbean

The sustainability of territorial agri-food systems depends on whether high-value produce can reach a paying market. The yam supply chain of Montes de María, a post-conflict subregion of the Colombian Caribbean, sorts its product into a non-substitutable export grade and a local grade. This study identifies the structural conditions under which single-point dependence transforms a demand shock into food loss, integrating network analysis with a household survey of the territory. The chain is modeled as a weighted directed graph in three layers: value concentration, structural criticality via Menger edge connectivity, and a differential-equation model of export-grade erosion under a demand shock with saturating absorption and storage; a parallel food-insecurity and dietary-diversity survey sets the baseline. Results, reported as conditional scenarios, show the export value hangs on a single non-redundant channel: one cut disconnects it. Under a shock, permanent loss nears 18% of diverted product versus 50% without storage, while the export-income collapse (40–57%) is not buffered. With 41% of surveyed households food-insecure, this fragility can erode rural livelihoods through economic access. Diversifying the export outlet and strengthening local storage emerge as levers for a resilient and sustainable chain, supporting the access dimension of food security that underpins territorial peace.