We report on the demonstration of MOVPE-grown single nanowire InGaN/GaN core-shell light emitting diodes (LEDs) with a transparent graphene contact for hole injection. The electrical homogeneity of the graphene-contacted LED has been assessed by electron beam induced current microscopy. By comparing graphene-contacted and metal-contacted nanowire LEDs, we show that the contact layout determines the electroluminescence spectrum. The electroluminescence changes color from green to blue with increasing injection current. High-resolution cathodoluminescence on cleaved nanowires allows the location with high precision of the origin of different emitted wavelengths and demonstrates that the blue peak originates from the emission of the radial quantum well on the m-planes, whereas the green peak arises from the In-rich region at the junction between the m-planes and the semipolar planes. The spectral behavior of the electroluminescence is understood by modeling the current distribution within the nanowire.