  The problem of electron scattering on the one-dimensional complexes is
considered. We propose a novel theoretical approach to solution of the
transport problem for a quantum graph. In the frame of the developed approach
the solution of the transport problem is equivalent to the solution of a linear
system of equations for the \emph{vertex amplitudes} $\mathbf{\Psi}$. All major
properties, such as transmission and reflection amplitudes, wave function on
the graph, probability current, are expressed in terms of one
$\mathbf{\Gamma}$-matrix that determines the transport through the graph. The
transmission resonances are analyzed in detail and comparative analysis with
known results is carried out.
