We consider the problem of similarity queries in biological network databases. Given a database of networks, similarity query returns all the database networks whose similarity (i.e. alignment score) to a given query network is at least a specified similarity cutoff value. Alignment of two networks is a very costly operation, which makes exhaustive comparison of all the database networks with a query impractical. To tackle this problem, we develop a novel indexing method, named RINQ (Reference-based Indexing for Biological Network Queries). Our method uses a set of reference networks to eliminate a large portion of the database quickly for each query. A reference network is a small biological network. We precompute and store the alignments of all the references with all the database networks. When our database is queried, we align the query network with all the reference networks. Using these alignments, we calculate a lower bound and an approximate upper bound to the alignment score of each database network with the query network. With the help of upper and lower bounds, we eliminate the majority of the database networks without aligning them to the query network. We also quickly identify a small portion of these as guaranteed to be similar to the query. We perform pairwise alignment only for the remaining networks. We also propose a supervised method to pick references that have a large chance of filtering the unpromising database networks. Extensive experimental evaluation suggests that (i) our method reduced the running time of a single query on a database of around 300 networks from over 2 days to only 8 h, (ii) our method outperformed the state of the art method Closure Tree and SAGA by a factor of three or more, and (iii) our method successfully identified statistically and biologically significant relationships across networks and organisms.