Abstract: Many physical problems described in terms of different nonlinear evolution equations formulated on low-dimensional domains. An important problem in modeling particle and wave dynamics within such approaches is controlling the wave propagation, e.g. avoiding the backscattering on domainâ€™s boundary. This can be done by imposing artificial boundary conditions. These artificial boundary conditions are constructed with the objective to approximate the exact solution of the whole-space problem, restricted to the interval. Such boundary conditions are called transparent boundary conditions. The approach has found its application in development of effective models providing tools for tunable wave transport in low-dimensional domains. Here we consider the problem of the absence of backscattering in the transport of solitons in low-dimensional networks modeled in terms of metric graphs. This approach allows to derive simple constraints, which link the equivalent usual Kirchhoff-type vertex conditions to the transparent ones.