The dynamics of solitary water waves is studied in two-dimensional open channels with a branching point. We rationalize the wave characteristics at a branching point by using the Jacobian |J| of the Schwarz-Christoffel transformation. It is observed that |J| acts in a similar fashion as a topography. Computational results illustrate the two-dimensional reflection-transmission wave-dynamics at the branching point, which are then compared to a reduced one-dimensional model for solitary waves on a graph/network. An approximate compatibility condition is used at the node of the 1D graph. Numerical experiments show that the one-dimensional graph-like model captures well the effective reflection-transmission properties of the solitary wave. Different regimes are considered though various values of branching angles and channel widths.