Abstract:
We prove some exponential Chebyshev inequality and derive the large deviation principle and the law of large numbers for the graphons constructed from a sequence of Erdős–Rényi random graphs with weights. Also, we obtain a new version of the large deviation principle for the number of triangles included in an Erdős–Rényi graph.
Keywords:Erdős–Rényi graph, graphon, large deviation principle, law of large numbers.