3D Gaussian Splatting (3DGS) provides an efficient method for high-quality scene reconstruction using anisotropic Gaussians. Recently, 3DGS-based methods have significantly improved the rendering quality of human avatars while enabling real-time performance. However, existing methods suffer from a magnitude mismatch in the number of Gaussians generated by image-based and 3DMM-based approaches. This discrepancy results in reconstructed expressions that lack fine-grained detail. In this paper, we introduce a novel method for reconstructing an animatable head avatar from a single image. We propose a Graph splitting network to progressively generate Gaussians from coarse to fine using an autoregressive architecture. To address the graph inconsistency caused by split Gaussians, we employ a mesh topology extension method to align the GNN's connectivity with the increased Gaussian count. Furthermore, we introduce a novel density control method that includes a gating mechanism that generates soft masks for Gaussians, preventing over-densification after the splitting operation. This allows for dynamic control over Gaussian density across different facial regions. For smooth and rapid training, we employ a delayed filtering strategy to avoid re-computing the graph topology during training. Experimental results demonstrate that our autoregressive structure effectively improves expression representation ability by progressively splitting Gaussians. This process, enabled by the GNN-guided splitting, synthesizes more precise facial details and achieves higher reconstruction quality.