In this paper we describe a problem of discovering query clusters from a click-through graph of web search logs. The graph consists of a set of web search queries, a set of pages selected for the queries, and a set of directed edges that connects a query node and a page node clicked by a user for the query. The proposed method extracts all maximal bipartite cliques (bicliques) from a click-through graph and compute an equivalence set of queries (i.e., a query cluster) from the maximal bicliques. A cluster of queries is formed from the queries in a biclique. We present a scalable algorithm that enumerates all maximal bicliques from the click-through graph. We have conducted experiments on Yahoo web search queries and the result is promising. Categories and Subject Descriptors H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval - Clustering; G.2.2 [Discrete Mathematics Graph Theory]: Graph Theory ? Graph algorithms General Terms Algorithms, Experimentation