With the rapid growth of usage of social network, the patterns, the scales, and the rate of information exchange have brought profound impacts on research and practice in finance. One important topic is the stock market efficiency analysis. Traditional schemes in finance focus on identifying significant abnormal returns triggered by important events. However, those events are merely identified by regular financial announcements such as mergers, equity issuances, and financial reports. Related data-driven approaches mainly focus on developing trading strategies using social media data, while the results are usually lack of theoretical explanations. In this paper, we fill the gap between the usage of social media data and financial theories. We propose a Degree of Social Attention (DSA) framework for stock analysis based on influence propagation model. Specifically, we define the self-influence for users in a social network and the DSA for stocks. A recursive process is also designed for dynamic value updating. Furthermore, we provide two modified approaches to reduce the computational cost. Our testing results from the Chinese stock market suggest that the proposed framework effectively captures stock abnormal returns based on the related social media data, and DSA is verified to be a key factor to link social media activities to the stock market.