<p>Delving into food security and food supply resilience requires a deep insight of the international crop trade dynamics, yet the complex patterns behind them are currently in the mist. This paper examines the determinants of the international crop trade networks, where complex dependencies and higher-order effects originating from hierarchical structures and temporal effects can be captured. With a comprehensive indicator and the clique percolation method, we identify vital countries and detect overlapping trade communities. By introducing a family of exponential random graph models to complement the traditional gravity model, our results suggest that the formation of the international crop trade is highly correlated with endogenous structural effects, internal actor-attribute effects, external embedding effects, and temporal effects. Our findings support the impeding effects of the hierarchical structure on trade formation from endogenous network statistics and the depth of economic integration. Furthermore, delayed reciprocity and stability contribute to the formation of international crop trade.</p>