Based on experience in PA 4, a few useful things that should be easy are:
Iterating over vertices and edges
getting incoming/outgoing edges
parallelizing and scheduling operations on graphs efficiently
ajayram
Adding on to @ufxela, we would also want a library to make chunking and synchronization of workloads amongst threads easier. For example, an easy way to define a map and reduce on a set of vertices or edges would be very helpful.
swkonz
leap frogging off of the above, we'd also need minimalist primitives for representing nodes in the graph such that users could compose complex graphs from small primitives.
Based on experience in PA 4, a few useful things that should be easy are: