Graham was born in Oodnadatta in far north South Australia and his family are Yankunytjatjara.
Graham is the Chief Executive Officer of Aboriginal Community Care SA (ACCSA). ACCSA is the largest aged care service provider for Aboriginal and Torres Strait Islander Elders in Adelaide and South Australia and provides a full continuum of aged care services from basic Commonwealth Home Support Program, Home Care Packages and Residential Care. ACCSA has a Community Visitor Scheme that provides visitors to socially isolated Elders. Services are provided in Adelaide and the APY lands in the far north of South Australia.