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We propose an end-to-end solution to address the problem of object localisation in partial scenes, where we aim to estimate the position of an object in an unknown area given only a partial 3D scan of the scene. We propose a novel scene representation to facilitate the geometric reasoning, Directed Spatial Commonsense Graph (D-SCG), a spatial scene graph that is enriched with additional concept nodes from a commonsense knowledge base. Specifically, the nodes of D-SCG represent the scene objects and the edges are their relative positions. Each object node is then connected via different commonsense relationships to a set of concept nodes. With the proposed graph-based scene representation, we estimate the unknown position of the target object using a Graph Neural Network that implements a novel attentional message passing mechanism. The network first predicts the relative positions between the target object and each visible object by learning a rich representation of the objects via aggregating both the object nodes and the concept nodes in D-SCG. These relative positions then are merged to obtain the final position. We evaluate our method using Partial ScanNet, improving the state-of-the-art by 5.9% in terms of the localisation accuracy at a 8x faster training speed.