Sharp Threshold for the Frechet Mean (or Median) of Inhomogeneous Erdos-Renyi Random Graphs. (arXiv:2201.11954v1 [math.PR])

Web: http://arxiv.org/abs/2201.11954

We address the following foundational question: what is the population, and
sample, Frechet mean (or median) graph of an ensemble of inhomogeneous
Erdos-Renyi random graphs? We prove that if we use the Hamming distance to
compute distances between graphs, then the Frechet mean (or median) graph of an
ensemble of inhomogeneous random graphs is obtained by thresholding the
expected adjacency matrix of the ensemble. We show that the result also holds
for the sample mean (or median) when the population …

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