The Number of Triangles in Random Intersection Graphs
Liang Dong , Zhishui Hu
Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (4) : 695 -725.
The Number of Triangles in Random Intersection Graphs
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.
Random intersection graph / Stein’s method / Poisson approximation / Normal approximation
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