Transport and optical properties of random networks of c-axis oriented wedge-shaped GaN nanowalls grown spontaneously on c-plane sapphire substrates through molecular beam epitaxy are investigated. Our study suggests a one dimensional confinement of carriers at the top edges of these connected nanowalls, which results in a blue shift of the band edge luminescence, a reduction of the exciton-phonon coupling, and an enhancement of the exciton binding energy. Not only that, the yellow luminescence in these samples is found to be completely suppressed even at room temperature. All these changes are highly desirable for the enhancement of the luminescence efficiency of the material. More interestingly, the electron mobility through the network is found to be significantly higher than that is typically observed for GaN epitaxial films. This dramatic improvement is attributed to the transport of electrons through the edge states formed at the top edges of the nanowalls.