Transfer entropy measures the strength and direction of information flow between different time series. We study the information flow networks of the Chinese stock market and identify important sectors and information flow paths. This paper uses the daily closing price data of the 28 level-1 sectors from Shenyin & Wanguo Securities ranging from 2000 to 2017 to study the information transmission between different sectors. We construct information flow networks with the sectors as the nodes and the transfer entropy between them as the corresponding edges. Then we adopt the maximum spanning arborescence (MSA) to extract important information flows and the hierarchical structure of the networks. We find that, during the whole sample period, the composite sector is an information source of the whole stock market, while the nonbank financial sector is the information sink. We also find that the non-bank finance, bank, computer, media, real estate, medical biology and non-ferrous metals sectors appear as high-degree root nodes in the outgoing and incoming information flow MSAs. Especially, the non-bank finance and bank sectors have significantly high degrees after 2008 in the outgoing information flow networks. We uncover how stock market turmoils affect the structure of the MSAs. Finally, we reveal the specificity of information source and sink sectors and make a conclusion that the root node sector acts as the information sink of the incoming information flow networks. Overall, our analyses show that the structure of information flow networks changes with time and the market exhibits a sector rotation phenomenon. Our work has important implications for market participants and policy makers in managing market risks and controlling the contagion of risks.