  Small diameter asymptotics is obtained for scattering solutions in a network
of thin fibers. The asymptotics is expressed in terms of solutions of related
problems on the limiting quantum graph. We calculate the Lagrangian gluing
conditions at vertices for the problems on the limiting graph. If the frequency
of the incident wave is above the bottom of the absolutely continuous spectrum,
the gluing conditions are formulated in terms of the scattering data for each
individual junction of the network.
