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1. LAGraph: A Community Effort to Collect Graph Algorithms Built on Top of the GraphBLAS

   Mattson, Timothy ; Davis, Timothy A. ; Kumar, Manoj ; Buluç, Aydin ; McMillan, Scott ; Moreira, José ; Yang, Carl ( May 2019 , Proceedings of the Workshop on Graphs, Architectures, Programming, and Learning)

   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. 

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2. A GraphBLAS Implementation of Triangle Centrality

   https://doi.org/10.1109/HPEC49654.2021.9622806  

   Li, Fuhuan ; Bader, David A. ( September 2021 , The 25th Annual IEEE High Performance Extreme Computing Conference (HPEC))

   Identifying key members in large social network graphs is an important graph analytic. Recently, a new centrality measure called triangle centrality finds members based on the triangle support of vertices in graph. In this paper, we describe our rapid implementation of triangle centrality using Graph-BLAS, an API specification for describing graph algorithms in the language of linear algebra. We use triangle centrality’s algebraic algorithm and easily implement it using the SuiteSparse GraphBLAS library. A set of experiments on large, sparse graph datasets is conducted to verify the implementation. 

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3. A Roadmap for the GraphBLAS C++ API

   https://doi.org/10.1109/IPDPSW50202.2020.00049  

   Brock, Benjamin ; Buluc, Aydin ; Mattson, Timothy G. ; McMillan, Scott ; Moreira, Jose E. ( May 2020 , GrAPL: Workshop on Graphs, Architectures, Programming, and Learning (IPDPSW))

   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. 

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4. LAGraph: Linear Algebra, Network Analysis Libraries, and the Study of Graph Algorithms

   https://doi.org/10.1109/IPDPSW52791.2021.00046  

   Szarnyas, Gabor ; Bader, David A. ; Davis, Timothy A. ; Kitchen, James ; Mattson, Timothy G. ; McMillan, Scott ; Welch, Erik ( June 2021 , 2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW))

   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. 

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5. Design of the GraphBLAS API for C

   https://doi.org/10.1109/IPDPSW.2017.117  

   Buluc, Aydin ; Mattson, Tim ; McMillan, Scott ; Moreira, Jose ; Yang, Carl ( May 2017 , Graph Algorithms Building Blocks)

   The purpose of the GraphBLAS Forum is to standardize linear-algebraic building blocks for graph computations. An important part of this standardization effort is to translate the mathematical specification into an actual Application Programming Interface (API) that (i) is faithful to the mathematics and (ii) enables efficient implementations on modern hardware. This paper documents the approach taken by the C language specification subcommittee and presents the main concepts, constructs, and objects within the GraphBLAS API. Use of the API is illustrated by showing an implementation of the betweenness centrality algorithm. 

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