Graph-based ranking for keyphrase extraction has become an important approach for measuring saliency scores in text due to its ability to capture the context. By modeling words as vertices and the co-occurrence relation between words as edges, the importance of words is measured from the whole graph. However, graphs by nature can only capture the pair-wise relation between vertices. Therefore, it is not clear if graphs can capture high-order relations of more than two words. In this paper, we propose to use a hypergraph to capture high-order relations appearing in short documents, and use such information to infer better ranking of words. Additionally, we model the temporal and social attributes of short documents and discriminative weights of words into the hypergraph as weights which give us the ability of capturing recent and topical keyphrases. Furthermore, to rank vertices in the proposed hypergraph, we propose a probabilistic random walk that takes into account weights of both vertices and hyperedges. We show the effectiveness of our approach by conducting extensive experiments over two different data sets which demonstrate the robustness of the proposed approach.