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

Abstract

We obtain an estimate of the convergence rate in the central limit theorem for the number of triangles in an heterogeneous Erdős-Rényi graphs. Our approach is reminiscent of Hoeffding decomposition (a common technique in the theory of U–statistics). We demonstrate that the centered and normalized number of triangles asymptotically behaves as well as the normalized sum of centered independent random variables, as the number of vertices of the graph increases. The proposed method is characterized by its simplicity and probabilistic intuition.