Ripple

Ripple is an open-source software project for developing and implementing a protocol for an open decentralized payment network. In its extreme form, the Ripple network could be a peer-to-peer distributed social network service with a monetary honor system based on trust that already exists between people in real-world social networks. The project was started by Ryan Fugger, who also wrote some good articles about it.

Modern monetary systems are built on obligations of the participants to each other. Cash and bonds are government obligations, and loan agreements are the personal obligations of borrowers. Bank account balances are bank obligations, backed by borrower and government obligations. For an obligation to have value, the holder must trust that the issuer can supply that value. Thus the banking network can be described as a trust network.

Ripple trust metric
There is no trust metric defined for Ripple, since it is not required for its functioning. However there is a Ripple Intermediary Path Search Algorithm for finding credit paths between nodes in the Ripple network.

Ripple trust network dataset
It should be easy to get it and in the best interest of Ripple to get it studied and published, though probably at the moment there are not too many nodes.