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  1. In graph analytics, a truss is a cohesive subgraph based on the number of triangles supporting each edge. It is widely used for community detection applications such as social networks and security analysis, and the performance of truss analytics highly depends on its triangle counting method. This paper proposes a novel triangle counting kernel named Minimum Search (MS). Minimum Search can select two smaller adjacency lists out of three and uses fine-grained parallelism to improve the performance of triangle counting. Then, two basic algorithms, MS-based triangle counting, and MS-based support updating are developed. Based on the novel triangle counting kernel and the two basic algorithms above, three fundamental parallel truss analytics algorithms are designed and implemented to enable different kinds of graph truss analysis. These truss algorithms include an optimized K-Truss algorithm, a Max-Truss algorithm, and a Truss Decomposition algorithm. Moreover, all proposed algorithms have been implemented in the parallel language Chapel and integrated into an open-source framework, Arkouda. Through Arkouda, data scientists can efficiently conduct graph analysis through an easy-to-use Python interface and handle large-scale graph data in powerful back-end computing resources. Experimental results show that the proposed methods can significantly improve the performance of truss analysis on real-world graphs compared with the existing and widely adopted list intersection-based method. The implemented code is publicly available from GitHub (https://github.com/Bears-R-Us/arkoudanjit). } 
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  2. 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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  3. Due to the emergence of massive real-world graphs, whose sizes may extend to terabytes, new tools must be developed to enable data scientists to handle such graphs efficiently. These graphs may include social networks, computer networks, and genomes. In this paper, we propose a novel graph package, Arachne, to make large-scale graph analytics more effortless and efficient based on the open-source Arkouda framework. Arkouda has been developed to allow users to perform massively parallel computations on distributed data with an interface similar to NumPy. In this package, we developed a fundamental sparse graph data structure and then built several useful graph algorithms around our data structure to form a basic algorithmic library. Benchmarks and tools were also developed to evaluate and demonstrate the use of our graph algorithms. The graph algorithms we have implemented thus far include breadth-first search (BFS), connected components (CC), k-Truss (KT), Jaccard coefficients (JC), triangle counting (TC), and triangle centrality (TCE). Their corresponding experimental results based on realworld and synthetic graphs are presented. Arachne is organized as an Arkouda extension package and is publicly available on GitHub (https://github.com/Bears-R-Us/arkouda-njit). 
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