This paper proposes AIGer, a novel method for effectively modeling And-Inverter Graphs (AIGs) to enhance the efficiency of logic circuit design automation in the field of electronic design automation (EDA). To address the limitations of existing methods, which lack joint modeling of functional and structural features and their limited dynamic information propagation, AIGer consists of a node-logic feature initialization embedding component and an AIG feature learning network component. The former projects logical nodes, such as AND and NOT, into an independent semantic space, enabling effective node embedding. The latter utilizes a heterogeneous graph convolutional network to design a dynamic relational weight matrix and a differentiated information aggregation method, thereby better representing the original structure and information of AIGs. Experimental results demonstrate that AIGer significantly improves the MAE and MSE compared to existing state-of-the-art models in signal probability prediction (SSP) and truth-table distance prediction (TTDP) tasks.