This paper describes the fabrication and design principles for using transparent graphene interconnects in stretchable arrays of microscale inorganic light emitting diodes (LEDs) on rubber substrates. We demonstrate several appealing properties of graphene for this purpose, including its ability to spontaneously conform to significant surface topography, in a manner that yields effective contacts even to deep, recessed device regions. Mechanics modeling reveals the fundamental aspects of this process, as well as the use of the same layers of graphene for interconnects designed to accommodate strains of 100% or more, in a completely reversible fashion. These attributes are compatible with conventional thin film processing and can yield highperformance devices in transparent layouts. Graphene interconnects possess attractive features for both existing and emerging applications of LEDs in information display, biomedical systems, and other environments.