Topic detection in social media is a challenging task due to the large-scale short and informal nature of messages. Existing methods choose to integrate structure or contexts among posts to alleviate the data sparsity of short text, however they ignore the spread characteristics of topics. A topic can spread in depth-wise and width-wise way on social networks. Specifically, wide dispersion gives priority to the paths that will spread to the low-order neighborhood, while deep propagation may spread to the more distant users along the propagation chains. Therefore, we propose a Dual-streams Graph convolution networks based Topic Model (DGTM) for microblog conversations. It aims to learn the contexts with full spread mode feature to alleviate data sparsity of microblog posts. Firstly, a user-level social network with posts information is built by the user interactions. Then, we design a dual-streams graph convolution networks module to learn the context-richer node embeddings by modeling spread characteristics. Lastly, the variational auto-encoder (VAE) is used to fuse the features of two spread modes and generate the more coherent topics. The experiments on three real-world datasets validate the effectiveness of our proposed model.