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The Number of Triangles in Random Intersection Graphs

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Abstract

Let \(T_n\) be the number of triangles in the random intersection graph G(n, m, p). When the mean of \(T_n\) is bounded, we obtain an upper bound on the total variation distance between \(T_n\) and a Poisson distribution. When the mean of \(T_n\) tends to infinity, the Stein–Tikhomirov method is used to bound the error for the normal approximation of \(T_n\) with respect to the Kolmogorov metric.

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Acknowledgements

We thank the two anonymous referees for their useful suggestions that greatly improved the presentation of this work. This work is supported by NSFC (Grant No. 11671373).

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  1. International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, People’s Republic of China

    Liang Dong & Zhishui Hu

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  1. Liang Dong
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  2. Zhishui Hu
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Correspondence to Zhishui Hu.

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Dong, L., Hu, Z. The Number of Triangles in Random Intersection Graphs. Commun. Math. Stat. 11, 695–725 (2023). https://doi.org/10.1007/s40304-021-00270-7

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