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In this paper, we consider a sequence of open quantum graphs, with uniformlybounded data, and we are interested in the asymptotic distribution of theirscattering resonances. Supposing that the number of leads in our quantum graphsis small compared to the total number of edges, we show that most resonancesare close to the real axis. More precisely, the asymptotic distribution ofresonances of our open quantum graphs is the same as the asymptoticdistribution of the square-root of the eigenvalues of the closed quantum graphsobtained by removing all the leads.

Scattering resonances of large weakly open quantum graphs