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Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find triangles more efficiently. We use a breadth-first search (BFS) to quickly generate a compact cover-edge set. Novel sequential and parallel triangle counting algorithms are presented that employ cover-edge sets. The sequential algorithm avoids unnecessary triangle-checking operations, and the parallel algorithm is communication-efficient. The parallel algorithm can asymptotically reduce communication on massive graphs such as from real social networks and synthetic graphs from the Graph500 Benchmark. In our estimate from massive-scale Graph500 graphs, our new parallel algorithm can reduce the communication on a scale 36 graph by 1156x and on a scale 42 graph by 2368x.
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This content will become publicly available on November 1, 2026
Cover Edge-Based Novel Triangle Counting
Counting and listing triangles in graphs is a fundamental task in network analysis, supporting applications such as community detection, clustering coefficient computation, k-truss decomposition, and triangle centrality. We introduce the cover-edge set, a novel concept that eliminates unnecessary edges during triangle enumeration, thereby improving efficiency. This compact cover-edge set is rapidly constructed using a breadth-first search (BFS) strategy. Using this concept, we develop both sequential and parallel triangle-counting algorithms and conduct comprehensive comparisons with state-of-the-art methods. We also design a benchmarking framework to evaluate our sequential and parallel algorithms in a systematic and reproducible manner. Extensive experiments on the latest Intel Xeon 8480+ processor reveal clear performance differences among algorithms, demonstrate the benefits of various optimization strategies, and show how graph characteristics, such as diameter and degree distribution, affect algorithm performance. Our source code is available on GitHub.
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- PAR ID:
- 10655188
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Algorithms
- Volume:
- 18
- Issue:
- 11
- ISSN:
- 1999-4893
- Page Range / eLocation ID:
- 685
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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