This investigation is a continuation of earlier work on the dynamics of the magnetic network. In a previous calculation (Hasan et al. 2005), we examined the response of a single flux tube to transverse motions of its footpoints. We now extend this analysis to a more realistic model of the network consisting of multiple flux tubes. We apply a transverse velocity perturbation uniformly along the lower boundary located at the base of the photosphere. Our 2-D MHD simulations enable us to study the complex wave pattern due to waves generated in the individual tubes as well as their interaction with those emanating from adjacent tubes. Our results show that the dominant heating of the chromosphere occurs due to slow magnetoacoustic waves in a region that is close to the central region of the flux tube.