AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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For any fixed $k$, we prove a lower bound on the $k$th largest modulus of an eigenvalue of the non-backtracking matrix $B$. Specifically, consider any deterministic or random family of graphs that converges locally to the unimodular Galton-Watson tree with root degree distribution $D$, and set $\kappa:=\mathbb E[D(D-1)...
The Bethe-Hessian is a symmetric matrix for which the negative spectrum has been observed to encode the informative structure of sparse stochastic block models. We prove that, in the stochastic block model where all vertices have expected degree $d>1$, the number of negative eigenvalues of the Bethe-Hessian is exactly...
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