There has been an explosion of hyperlinked data in many domains, e.g., the biological Web. Expressive query languages and effective ranking techniques are required to convert this data into browsable knowledge. We propose the Graph Information Discovery (GID) framework to support sophisticated user queries on a rich web of annotated and hyperlinked data entries, where query answers need to be ranked in terms of some customized ranking criteria, e.g., PageRank or ObjectRank. GID has a data model that includes a schema graph and a data graph, and an intuitive query interface. The GID framework allows users to easily formulate queries consisting of sequences of hard filters (selection predicates) and soft filters (ranking criteria); it can also be combined with other specialized graph query languages to enhance their ranking capabilities. GID queries have a well-defined semantics and are implemented by a set of physical operators, each of which produces a ranked result graph. We discuss ...