Graph Algorithms in the Language of Linear Algebra: How Did We Get Here, and Where Do We Go Next?

Numerical computational science dominated the first half century of high- performance computing; graph theory served numerical linear algebra by enabling efficient sparse matrix methods. Turnabout is fair play: Nowadays more and more computational problems concern graphs in their own right, and sparse matrix methods are often a good way to look at algorithms on graphs. This has led via a long path to the Graph BLAS and its reference implementations, which are a significant milestone. But there's a lot left to do. What happens now?