# An Independent Process Approximation to Sparse Random Graphs with a Prescribed Number of Edges and Triangles

@article{Desalvo2015AnIP, title={An Independent Process Approximation to Sparse Random Graphs with a Prescribed Number of Edges and Triangles}, author={Stephen Desalvo and Michaela Puck Rombach}, journal={arXiv: Probability}, year={2015} }

We prove a $pre$-$asymptotic$ bound on the total variation distance between the uniform distribution over two types of undirected graphs with $n$ nodes. One distribution places a prescribed number of $k_T$ triangles and $k_S$ edges not involved in a triangle independently and uniformly over all possibilities, and the other is the uniform distribution over simple graphs with exactly $k_T$ triangles and $k_S$ edges not involved in a triangle. As a corollary, for $k_S = o(n)$ and $k_T = o(n)$ as…

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