The sustainability of supply chain plays a key role in achieving optimal performance in controlling the supply chain. The management of risks that occur in a supply chain is a fundamental problem for the purpose of developing the sustainability of the network and elevating the performance efficiency of the supply chain. The correct classification of products is another essential element in a sustainable supply chain. Acknowledging recent breakthroughs in the context of deep networks, several architectural options have been deployed to analyze supply chain datasets. A novel geometric deep network is used to propose an ensemble deep network. The proposed Chebyshev ensemble geometric network (Ch-EGN) is a hybrid convolutional and geometric deep learning. This network is proposed to leverage the information dependencies in supply chain to derive invisible states of samples in the database. The functionality of the proposed deep network is assessed on the two different databases. The SupplyGraph Dataset and DataCo are considered in this research. The prediction of delivery status of DataCo supply chain is done for risk administration. The product classification and edge classification are performed using the SupplyGraph database to enhance the sustainability of the supply network. An average accuracy of 98.95% is obtained for the ensemble network for risk management. The average accuracy of 100% and 98.07% are obtained for sustainable supply chain in terms of 5 product group classification and 4 product relation classification, respectively. The average accuracy of 92.37% is attained for 25 company relation classification. The results confirm an average improvement and efficiency of the proposed method compared to the state-of-the-art approaches.