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The K-Truss of a graph is a cohesive subgraph that has been widely used for community detection in applications such as social networks and security analysis. In this paper, we first propose one optimized triangle search kernel with a few operations that can be used in both triangle counting and triangle search to replace the existing list intersection method. Based on the optimized kernel, three truss analytics algorithms, an optimized K-Truss parallel algorithm, a maximal K-Truss parallel algorithm, and a Truss decomposition parallel algorithm, are developed to efficiently enable different kinds of graph analysis. Moreover, all proposed parallel algorithms have been implemented in the highly-productive parallel language Chapel and integrated into the open-source framework Arkouda. Experimental results compared with the existing list intersection-based method show that for both synthetic and real-world graphs, the proposed method can significantly improve the performance of truss analysis on large graphs. The implemented method is publicly available from GitHub. 

Data from emerging applications, such as cybersecurity and social networking, can be abstracted as graphs whose edges are updated sequentially in the form of a stream. The challenging problem of interactive graph stream analytics is the quick response of the queries on terabyte and beyond graph stream data from end users. In this paper, a succinct and efficient double index data structure is designed to build the sketch of a graph stream to meet general queries. A single pass stream model, which includes general sketch building, distributed sketch based analysis algorithms and regression based approximation solution generation, is developed, and a typical graph algorithm—triangle counting—is implemented to evaluate the proposed method. Experimental results on power law and normal distribution graph streams show that our method can generate accurate results (mean relative error less than 4%) with a high performance. All our methods and code have been implemented in an open source framework, Arkouda, and are available from our GitHub repository, Bader-Research. This work provides the large and rapidly growing Python community with a powerful way to handle terabyte and beyond graph stream data using their laptops. 

We propose an implementation of the k-Truss algorithm in Arkouda that finds all maximal k-trusses in a graph. Arkouda is an open-source framework for large scale graph analytics that allows users to access a powerful server driven backend from their own personal computer.