In this paper, we explore an open research problem concerning the reconstruction of 3D scenes from images. Recent methods have adopt 3D Gaussian Splatting (3DGS) to produce 3D scenes due to its efficient training process. However, these methodologies may generate incomplete 3D scenes or blurred multiviews. This is because of (1) inaccurate 3DGS point initialization and (2) the tendency of 3DGS to flatten 3D Gaussians with the sparse-view input. To address these issues, we propose a novel framework EG-Gaussian, which utilizes epipolar geometry and graph networks for 3D scene reconstruction. Initially, we integrate epipolar geometry into the 3DGS initialization phase to enhance initial 3DGS point construction. Then, we specifically design a graph learning module to refine 3DGS spatial features, in which we incorporate both spatial coordinates and angular relationships among neighboring points. Experiments on indoor and outdoor benchmark datasets demonstrate that our approach significantly improves reconstruction accuracy compared to 3DGS-based methods.