Comprehensive visual understanding requires detection frameworks that can effectively learn and utilize object interactions while analyzing objects individually. This is the main objective in Human-Object Interaction (HOI) detection task. In particular, relative spatial reasoning and structural connections between objects are essential cues for analyzing interactions, which is addressed by the proposed Visual-Spatial-Graph Network (VSGNet) architecture. VSGNet extracts visual features from the human-object pairs, refines the features with spatial configurations of the pair, and utilizes the structural connections between the pair via graph convolutions. The performance of VSGNet is thoroughly evaluated using the Verbs in COCO (V-COCO) and HICO-DET datasets. Experimental results indicate that VSGNet outperforms state-of-the-art solutions by 8% or 4 mAP in V-COCO and 16% or 3 mAP in HICO-DET.