Summary form only given. A number of problems in information retrieval and natural language processing can be approached using graph theory. Some representative examples in IR include Brin and Page's Pagerank and Kleinberg's HITS for document ranking using graph-based random walk models. In NLP, one could mention Pang and Lee's work on sentiment analysis using graph min- cuts, Mihalcea's work on word sense disambiguation, Zhu et al.'s label propagation algorithms, Toutanova et al.'s prepositional attachment algorithm, and McDonald et al.'s dependency parsing algorithm using minimum spanning trees. In this talk I will quickly summarize three graph-based algorithms developed recently at the University of Michigan: (a) lexrank, a method for multidocument summarization based on random walks on lexical centrality graphs, (b) TUMBL, a generic method using bipartite graphs for semi-supervised learning, and (c) biased lexrank, a semi-supervised technique for passage ranking for information retrieval and discuss the applicability of such techniques to other problems in Natural Language Processing and Information Retrieval.