Current end-to-end Scene Graph Generation (SGG) relies solely on visual representations to separately detect sparse relations and entities in an image. This leads to the issue where the predictions of entities do not contribute to the prediction of relations, necessitating post-processing to assign corresponding subjects and objects to the predicted relations. In this paper, we introduce a sparse relationship matrix that bridges entity detection and relation detection. Our approach not only eliminates the need for relation matching, but also leverages the semantics and positional information of predicted entities to enhance relation prediction. Specifically, a multi-granularity sparse relationship matrix prediction network is proposed, which utilizes three gated pooling modules focusing on filtering negative samples at different granularities, thereby obtaining a sparse relationship matrix containing entity pairs most likely to form relations. Finally, a set of sparse, most probable subject-object pairs can be constructed and used for relation decoding. Experimental results on multiple datasets demonstrate that our method achieves a new state-of-the-art overall performance. Our code is available.