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Mikyška, J.; de Mulatier, C.; Paszynski, M.; Krzhizhanovskaya, V.V.; Dongarra, J.J.; Sloot, P.M. (Ed.)Triangles and squares count are widely-used graph analytic metrics providing insights into the connectivity of a graph. While the literature has focused on algorithms for global counts in simple graphs, this paper presents parallel algorithms for global and per-node triangle and square counts in large multigraphs. The algorithms have linear improvements in computational complexity as the number of cores increases. The triangle count algorithm has the same complexity as the best-known algorithm in the literature. The squares count algorithm has a lower execution time than previous methods. The proposed algorithms are evaluated on six real-world graphs and multigraphs, including protein-protein interaction graphs, knowledge graphs and large web graphs.more » « less
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Cappelletti, Luca; Fontana, Tommaso; Reese, Justin; Bader, David A. (, IEEE)This paper presents an algorithm for detecting attributed high-degree node isomorphism. High-degree isomorphic nodes seldom happen by chance and often represent duplicated entities or data processing errors. By definition, isomorphic nodes are topologically indistinguishable and can be problematic in graph ML tasks. The algorithm employs a parallel, “degree-bounded” approach that fingerprints each node’s local properties through a hash, which constrains the search to nodes within hash-defined buckets, thus minimising the number of comparisons. This method scales on graphs with billions of nodes and edges. Finally, we provide isomorphic node oddities identified in real-world data.more » « less
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