See here for a more current discussion.
HyperGraphDB is a Java database for storing hypergraphs in-memory and on disk. It is a planned component of the OpenCog Framework (complimenting the AtomTable as long-term storage, distributed access storage, and for specialized queries) but it is also intended to be usable by other projects as a stand-alone library.
Historically, HyperGraphDB's Java implementation (at http://code.google.com/p/hypergraphdb/) started as a prototype for the "real" C++ version. The challenge is to make a blazing fast C++ implementation that's compatible with the storage layout set forth by the Java version and that follows a similar architecture. HyperGraphDB was inspired in part by the paper "Semantic Integration and Querying of Heterogeneous Data Sources Using a Hypergraph Data Model" by Dimitri Theodoratos (http://books.google.com.au/books?id=BgMYPXYGK3EC&pg=PA166&ots=SRS8u2UgXL&sig=5kWwQNXfg_y0-2LsSA7Sy9xuzr0)
It is difficult to categorize HyperGraphDB as yet another database because much of its design evolves around providing the means to manage structure reach information with arbitrary layers of complexity. For instance, a relational as well as an object-oriented style of data management can be emulated. The design is minimalistic at its core and the end-goal is to evolve a set of concepts and practices, combining structure and interpretation in such a way as to allow future software to meet the complexities of the real-world better that now.
HypergraphDB C++ project: https://launchpad.net/hypergraphdb