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We investigate experimentally a Fermi golden rule in two-edge and five-edgemicrowave networks with preserved time reversal invariance. A Fermi golden rulegives rates of decay of states obtained by perturbing embedded eigenvalues ofgraphs and networks. We show that the embedded eigenvalues are connected withthe topological resonances of the analyzed systems and we find the trajectoriesof the topological resonances in the complex plane.

Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks