Subgraph discovery in a single data graph---finding subsets of vertices and edges satisfying a user-specified criteria---is an essential and general graph analytics operation with a wide spectrum of applications. Depending on the criteria, subgraphs of interest may correspond to cliques of friends in social networks, interconnected entities in RDF data, or frequent patterns in protein interaction networks to name a few. Existing systems usually examine a large number of subgraphs while employing many computers and often produce an enormous result set of subgraphs. How can we enable fast discovery of only the most relevant subgraphs while minimizing the computational requirements? We present Nuri, a general subgraph discovery system that allows users to succinctly specify subgraphs of interest and criteria for ranking them. Given such specifications, Nuri efficiently finds the k most relevant subgraphs using only a single computer. It prioritizes (i.e., expands earlier than others) subgraphs that are more likely to expand into the desired subgraphs (prioritized subgraph expansion) and proactively discards irrelevant subgraphs from which the desired subgraphs cannot be constructed (pruning). Nuri can also efficiently store and retrieve a large number of subgraphs on disk without being limited by the size of main memory. We demonstrate using both real and synthetic datasets that Nuri on a single core outperforms the closest alternative distributed system consuming 40 times more computational resources by more than 2 orders of magnitude for clique discovery and 1 order of magnitude for subgraph isomorphism and pattern mining.