A pre-relational databases datamodel. "Preceeded" by the relational model since the flexibility of this makes it hard to work with. Now re-invented in RDF :)
Graph mining refers to extracting knowledge from massive graphs. The data sets of telephone calls we see at AT&T can be viewed as a single graph, with several hundred million phone numbers as nodes, and calls between phone numbers as edges. It is a giant social network, like an internet connections graph or a rich citation network.