Abstract We study the number of triangles Tₙ in the sparse -model on n vertices, a random graph model that captures degree heterogeneity in real-world networks. Using the norms of the heterogeneity parameter vector, we first determine the asymptotic mean and variance of Tₙ. Next, by applying the Malliavin–Stein method, we derive a non-asymptotic upper bound on the Kolmogorov distance between the normalized Tₙ and the standard normal distribution. Under an additional assumption on degree heterogeneity, we further prove the asymptotic normality for Tₙ as n.
Zhang et al. (Tue,) studied this question.