Estimating causal effects is crucial for decision-makers in many applications, but it is particularly challenging with observational network data due to peer interactions. Some algorithms have been proposed to estimate causal effects involving network data, particularly peer effects, but they often fail to tell apart diverse peer effects. To address this issue, we propose a general setting which considers both peer direct effects and peer indirect effects, and the effect of an individual's own treatment, and provide the identification conditions of these causal effects and their proofs. To differentiate these effects, we leverage causal mediation analysis and tailor it specifically for network data. Furthermore, given the inherent challenges of accurately estimating effects in networked environments, we propose to incorporate attention mechanisms to capture the varying influences of different neighbors and to explore high-order neighbor effects using multi-layer graph neural networks (GNNs). Additionally, we employ the Hilbert-Schmidt Independence Criterion (HSIC) to further enhance the model’s robustness and accuracy. Extensive experiments on two semi-synthetic datasets based on real-world networks, as well as on recommendation system data confirm the effectiveness of our approach. Our theoretical findings have the potential to improve intervention strategies in networked systems, particularly in social networks and public health.