Computing on or over large graphs. Engines for calculating things on or about graphs. Which is everything, but, in particular, typically structures with of sparsity in some sense.
For specific applications of such computations, see e.g. graphical models or complex networks.

SNAP.py is engineered from the ground to do Stuff To Large Networks
 It plugs into snapvx, a ‘nearlyconvex’ solver for graphlike data.

Apache Giraph is a very large scale graph processor.
Apache Giraph is an iterative graph processing system built for high scalability. For example, it is currently used at Facebook to analyze the social graph formed by users and their connections. Giraph originated as the opensource counterpart to Pregel, the graph processing architecture developed at Google and described in a 2010 paper. Both systems are inspired by the Bulk Synchronous Parallel model of distributed computation introduced by Leslie Valiant. Giraph adds several features beyond the basic Pregel model, including master computation, sharded aggregators, edgeoriented input, outofcore computation, and more. With a steady development cycle and a growing community of users worldwide, Giraph is a natural choice for unleashing the potential of structured datasets at a massive scale. To learn more, consult the User Docs section above.

neo4j is the previous season's hot graph query system.
 graphlab, now a Turi product i think tries to solve general nongraphy ML problems but also… solves graphish ones? Do they also run a cloud? Or something? Maybe someone should actually read their website. I clearly didn't.

ASAP has some good background
Today, a deluge of graph processing frameworks exist, both in academia and opensource.[…] These frameworks typically provide highlevel abstractions that make it easy for developers to implement many graph algorithms. A vast majority of the existing graph processing frameworks however have focused on graph analysis algorithms. These frameworks are fast and can scale out to handle very large graph analysis settings: for instance, GraM can run one iteration of page rank on a trillionedge graph in 140 seconds in a cluster. In contrast, systems that support graph pattern mining fail to scale to even moderately sized graphs, and are slow, taking several hours to mine simple patterns