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Counterexamples to the Mao-Wu-Xu spectral conjecture and a three-scale boundary for spherical random graphs
Random geometric graph detection asks whether a graph generated from $n$ independent uniform points on $S^{d-1}$, with edge probabilities depending on inner products, can be distinguished from an Erdos-Renyi graph of the same edge density using only its adjacency matrix. Mao, Wu, and Xu conjectured
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