Recently many data types arising from data mining and Web search applications can be modeled as bipartite graphs. Examples include queries and URLs in query logs, and authors and papers in scientific literature. However, one of the issues is that previous algorithms only consider the content and link information from one side of the bipartite graph. There is a lack of constraints to make sure the final relevance of the score propagation on the graph, as there are many noisy edges within the bipartite graph. In this paper, we propose a novel and general Co-HITS algorithm to incorporate the bipartite graph with the content information from both sides as well as the constraints of relevance. Moreover, we investigate the algorithm based on two frameworks, including the iterative and the regularization frameworks, and illustrate the generalized Co-HITS algorithm from different views. For the iterative framework, it contains HITS and personalized PageRank as special cases. In the regularization framework, we successfully build a connection with HITS, and develop a new cost function to consider the direct relationship between two entity sets, which leads to a significant improvement over the baseline method. To illustrate our methodology, we apply the Co-HITS algorithm, with many different settings, to the application of query suggestion by mining the AOL query log data. Experimental results demonstrate that CoRegu-0.5 (i.e., a model of the regularization framework) achieves the best performance with consistent and promising improvements.