Scene graph generation aims to construct a semantic graph structure from an image such that its nodes and edges respectively represent objects and their relationships. One of the major challenges for the task lies in the presence of distracting objects and relationships in images; contextual reasoning is strongly distracted by irrelevant objects or backgrounds and, more importantly, a vast number of irrelevant candidate relations. To tackle the issue, we propose the Selective Quad Attention Network (SQUAT) that learns to select relevant object pairs and disambiguate them via diverse contextual interactions. SQUAT consists of two main components: edge selection and quad attention. The edge selection module selects relevant object pairs, i.e., edges in the scene graph, which helps contextual reasoning, and the quad attention module then updates the edge features using both edge-to-node and edge-to-edge cross-attentions to capture contextual information between objects and object pairs. Experiments demonstrate the strong performance and robustness of SQUAT, achieving the state of the art on the Visual Genome and Open Images v6 benchmarks.