There is increasing interest to apply graph analytical techniques to a wide array of problems, many operating on large-scale graphs with billions of edges. While graph algorithms and their complexity is textbook material, efficient implementation of such algorithms is still a major challenge due to a number of reasons. First, the irregular and unstructured nature of graphs leads to a massive amount of random data access, which makes it difficult to use typical caching and parallelization techniques. Second, to optimize their code, developers need to be aware of the nuances of the underlying hardware which, at the very least consists of multiple CPU cores but often also incorporates heterogeneous components such as GPUs or even FPGAs. During the last decade, a number of graph programming models (such as Google's Pregel) have been proposed but most of these focused defining high-level abstractions for distributed execution environments and introduced a significant runtime overhead.

A potential approach for defining efficient graph processing algorithms is to exploit the well-known duality of graphs and sparse adjacency matrices, using matrix operations to capture algorithms. Surprisingly, only a few recent research prototypes have used this model with little consensus on the set of necessary building blocks. The GraphBLAS initiative (launched in 2013) aims to define a standard to capture graph algorithms in the language of linear algebra - following the footsteps of the BLAS standard which, starting four decades ago, revolutionized scientific computing by defining constructs on dense matrices.

In this talk, I give an overview of the GraphBLAS standard and its key components. First, I illustrate how matrix operations on various semirings correspond to the steps in graph algorithms. I then use these operations to present fundamental graph algorithms such as breadth-first search, shortest paths, and the clustering coefficient. Finally, I demonstrate the scalability of the GraphBLAS-based algorithms with the LDBC Graphalytics benchmark. The presented implementations are available open-source as part of LAGraph, a library built on top of GraphBLAS to demonstrate how to design efficient algorithms in linear algebra.