The low light extraction efficiency (LEE) stemming from the transverse-magnetic dominant emission is one of the major factors limiting the performance of aluminum gallium nitride (AlGaN)-based deep ultraviolet (UV) light-emitting diodes (LEDs) when the light emission wavelengths are close to 200 nm. These wavelengths, nonetheless, are pivotal to applications including sensing and sterilization and are considered human safe. We investigate the LEE of AlGaN/AlN nanowire (NW) deep UV LEDs emitting at 225 nm, with a focus on the top-surface LEE by considering different NW arrangements, typical NW spacings and radii from AlGaN NWs grown by selective area epitaxy, the influence of Si on the LEE in comparison to an Al reflector, and graphene as the top electrode. Our results show that given the selected range of design parameters, the top-surface LEE for honeycomb, square, and hexagonal lattices can be up to around 42% for complete devices on Si with the graphene top electrode; and compared to using an Al reflector, the Si substrate does not reduce LEE considerably. In the end, the light extraction mechanism is discussed by simulating the two-dimensional photonic crystal band structures.