Given a large real-world graph where vertices are associated with labels, how do we quickly find interesting vertex sets according to a given query? In this paper, we study label-based proximity search in large graphs, which finds the top-k query-covering vertex sets with the smallest diameters. Each set has to cover all the labels in a query. Existing greedy algorithms only return approximate answers, and do not scale well to large graphs. We propose a novel framework, called gDensity, which uses density index and likelihood ranking to find vertex sets in an efficient and accurate manner. Promising vertices are ordered and examined according to their likelihood to produce answers, and the likelihood calculation is greatly facilitated by density indexing. Techniques such as progressive search and partial indexing are further proposed. Experiments on real-world graphs show the efficiency and scalability of gDensity. © 2012 ACM.