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A system of 'telegrapher's' equations for a number of long lines joined into a network is studied. Explicit formulas for Fourier transforms of current and voltage are derived. These formulas are very suitable for computer application as well as for the analytical study of processes on networks. As an example, the availability of formulas aids the derivation of explicit formulas for maxima of current amplitude over the given class of admissible external influences. These values may be used to indicate the characteristic of network robustness to excess voltage or electromagnetic impulse. The approach is based on the operational solution already proposed by the author for more general partial differential equations on graphs.