We focus on large graphs where nodes have attributes, such as a social network where the nodes are labelled with each person's job title. In such a setting, we want to find subgraphs that match a user query pattern. For example, a `star' query would be, "find a CEO who has strong interactions with a Manager, a Lawyer, and an Accountant, or another structure as close to that as possible". Similarly, a `loop' query could help spot a money laundering ring. Traditional SQL-based methods, as well as more recent graph indexing methods, will return no answer when an exact match does not exist. Our method can find exact-, as well as near-matches, and it will present them to the user in our proposed `goodness' order. For example, our method tolerates indirect paths between, say, the `CEO' and the `Accountant' of the above sample query, when direct paths do not exist. Its second feature is scalability. In general, if the query has nq nodes and the data gr...