Liver cancer remains a leading cause of global mortality, driving interest in computer-aided diagnosis for liver tumor detection. Existing methods typically focus on individual lesions and avoid the impact of neighboring tumors on diagnostic accuracy. This study introduces a novel multi-phase multi-graph (MPMG) approach to improve liver tumor classification using contrast-enhanced computed tomography (CECT) scans. The MPMG method models inter-lesion relationships, including the ratio of diameters, semantic similarity, physical distance, and neighbor influence score as graph edge embeddings, while multiphasic features extracted from a proposed deep convolutional neural network form the node representations. By analysing different edge embedding formations, we find through extensive experiments that the proposed MPMG model outperforms several state-of-the-art methods in liver tumor diagnosis.