High quality InN nanowires (NWs) were grown from nanoscale catalyst patterns by vapor-liquid-solid mechanism. The nanowires bend spontaneously or get deflected from other nanowires at multiples of 30deg forming nano-networks. Smooth and planar NWs used to fabricate field effect transistors (FET) exhibited excellent drain current modulation in a back-gated geometry. The mobility calculated from the I-V characteristics is 36 cm2/Vs, while the carrier concentration is 4.8times1018 cm-3. The NW FET based nanosensor demonstrated high sensitivity to trace NO2 due to a thin In2O3 shell layer present around the InN core. The adsorption of the NO2 molecules reduces the density of the carriers confined at the InN/In2O3 interface, thus reducing the drain current. The change in drain current for a single NW based FET resulted in a very high sensitivity of 45 ppb in ambient conditions. Planar InN nano-networks can potentially offer a much improved sensitivity to trace NO2 in ambient conditions.