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1. Fast Triangle Counting

   https://doi.org/10.1109/HPEC58863.2023.10363539  

   Bader, David A (September 2023, IEEE)

   Listing and counting triangles in graphs is a key algorithmic kernel for network analyses including community detection, clustering coefficients, k-trusses, and triangle centrality. We design and implement a new serial algorithm for triangle counting that performs competitively with the fastest previous approaches on both real and synthetic graphs, such as those from the Graph500 Benchmark and the MIT/Amazon/IEEE Graph Challenge. The experimental results use the recently-launched Intel Xeon Platinum 8480+ and CPU Max 9480 processors. 

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2. Fast Triangle Counting

   Bader, David (September 2023, The 27th Annual IEEE High Performance Extreme Computing Conference (HPEC))

   Listing and counting triangles in graphs is a key algorithmic kernel for network analyses including community detection, clustering coefficients, k-trusses, and triangle centrality. We design and implement a new serial algorithm for triangle counting that performs competitively with the fastest previous approaches on both real and synthetic graphs, such as those from the Graph500 Benchmark and the MIT/Amazon/IEEE Graph Challenge. The experimental results use the recently-launched Intel Xeon Platinum 8480+ and CPU Max 9480 processors. 

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3. Pascal’s Triangle Fractal Symmetries

   https://doi.org/10.1103/PhysRevLett.128.115301  

   Myerson-Jain, Nayan E.; Liu, Shang; Ji, Wenjie; Xu, Cenke; Vijay, Sagar (March 2022, Physical Review Letters)
4. Developability of triangle meshes

   https://doi.org/10.1145/3197517.3201303  

   Stein, Oded; Grinspun, Eitan; Crane, Keenan (July 2018, ACM Transactions on Graphics)
5. Triangle Centrality in Arkouda

   Joseph Patchett; Zhihui Du; Fuhuan Li; David A. Bader (September 2022, The 26th Annual IEEE High Performance Extreme Computing Conference (HPEC))

   There are a wide number of graph centrality metrics. Further, the performance of each can vary widely depending on the type of implementation. In this work we present our implementation of triangle centrality in Arkouda with several different triangle counting methods. Triangle Centrality is a robust metric that captures the centrality of a vertex through both a vertex’s own connectedness and that of its neighbors. Arkouda is an open-source framework for data science at the scale of terabytes and beyond. These methods are compared against each other and another shared memory implementation. 

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