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Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph algorithms with high-level algorithms common in network analysis. In this paper, we describe the first release of the LAGraph library, the design decisions behind the library, and performance using the GAP benchmark suite. LAGraph, however, is much more than a library. It is also a project to document and analyze the full range of algorithms enabled by the GraphBLAS. To that end, we have developed a compact and intuitive notation for describing these algorithms. In this paper, we present that notation with examples from the GAP benchmark suite. 

Data privacy within the context of heterogenous data and data management systems continues to be an important issue. At the Poly?19 workshop, held in conjunction with VLDB 2019 in Los Angeles, CA, one of the major themes explored was the implication of data privacy regulations such as GDPR to systems composed of multiple heterogenous databases. This summary outlines some of the major approaches and directions presented by various presenters during the privacy portion of the Poly?19 workshop. 

The GraphBLAS are building blocks for expressing graph algorithms in terms of linear algebra. Currently, the GraphBLAS are defined as a C API. Implementations of the GraphBLAS have exposed limitations in expressiveness and performance due to limitations in C. A move to C++ should address many of these limitations while providing a simpler API. Furthermore, for methods based on user-defined types and operators, the performance should be significantly better. C++has grown into a pervasive programming language across many domains. We see a compelling argument to define a GraphBLAS C++ API. This paper presents our roadmap for the development of a GraphBLAS C++ API. Open issues are highlighted with the goal of fostering discussion and generating feedback within the GraphBLAS user community to guide us as we develop the GraphBLAS C++ API. 

The GraphBLAS emerged from an international effort to standardize linear-algebraic building blocks for computing on graphs and graph-structured data. The GraphBLAS is expressed as a C API and has paved the way for multiple implementations. The GraphBLAS C API, however, does not define how distributed-memory parallelism should be handled. This paper reviews various approaches for a GraphBLAS API for distributed computing. This work is guided by our experience with existing distributed memory libraries. Our goal for this paper is to highlight the pros and cons of different approaches rather than to advocate for one particular choice. 

In 2013, we released a position paper to launch a community effort to define a common set of building blocks for constructing graph algorithms in the language of linear algebra. This led to the GraphBLAS. We released a specification for the C programming language binding to the GraphBLAS in 2017. Since that release, multiple libraries that conform to the GraphBLAS C specification have been produced. In this position paper, we launch the next phase of this ongoing community effort: a project to assemble a set of high level graph algorithms built on top of the GraphBLAS. While many of these algorithms are well-known with high quality implementations available, they have not been assembled in one place and integrated with the GraphBLAS. We call this project the LAGraph graph algorithms project and with this position paper, we put out a call for collaborators to join us. While the initial goal is to just assemble these algorithms into a single framework, the long term goal is a library of production-worthy code, with the LAGraph library serving as an open source repository of verified graph algorithms that use the GraphBLAS. 

The GraphBLAS C specification provisional release 1.0 is complete. To manage the scope of the project, we had to defer important functionality to a future version of the specification. For example, we are well aware that many algorithms benefit from an inspector-executor execution strategy. We also know that users would benefit from a number of standard predefined semirings as well as more general user-defined types. These and other features are described in this paper in the context of a future release of the GraphBLAS C API.