Localized eigenvectors on metric graphs

We analyze the eigenvectors of generalized Laplacian for two metric graphs occurring in practical applications. In accordance with random network theory, localization an eigenvector is rare and should be tuned to observe exactly localized eigenvectors. derive resonance conditions obtain various geometric configurations their combinations form more complicated resonant structures. These suggest new indicators based on energy density; contrast standard criteria, ours provide number active edges. also ways design resonating systems graphs. Finally, numerical simulations time-dependent wave equation graph show that can excited by a broadband initial condition, even leaky boundary conditions.