Graph Neural Networks (GNNs) have demonstrated great power in many network analytical tasks. However, graphs (i.e., networks) in the real world are usually text-rich, implying that valuable semantic information needs to be carefully considered. Existing GNNs for text-rich networks typically treat text as attribute words alone, which inevitably leads to the loss of important semantic structures, limiting the representation capability of GNNs. In this paper, we propose an end-to-end adaptive semantic architecture of graph convolutional networks, namely AS-GCN, which unifies neural topic model and graph convolutional networks, for text-rich network representation. Specifically, we utilize a neural topic model to extract the global topic semantics, and accordingly augment the original text-rich network into a tri-typed heterogeneous network, capturing both the local word-sequence semantic structure and the global topic semantic structure from text. We then design an effective semantic-aware propagation of information by introducing a discriminative convolution mechanism. We further propose two strategies, that is, distribution sharing and joint training, to adaptively generate a proper network structure based on the learning objective to improve network representation. Extensive experiments on text-rich networks illustrate that our new architecture outperforms the state-of-the-art methods by a significant improvement. Meanwhile, this architecture can also be applied to e-commerce search scenes, and experiments on a real e-commerce problem from JD further demonstrate the superiority of the proposed architecture over the baselines.