Note on normal approximation for number of triangles in heterogeneous Erdős-Rényi graph

We obtain a bound for the convergence rate in the central limit theorem for the number of triangles in a heterogeneous Erdős-Rényi graphs. Our approach is reminiscent of Hoeffding decomposition (a common technique in the theory of U-statistics). We show that the centered and normalized number of triangles asymptotically behaves as the normalized sum of centered independent random variables when the number of vertices increases. The proposed method is simple and intuitive.