Edgar Hugh Graham (19 January 1897 – 13 November 1957) was an Australian politician and a member of the New South Wales Legislative Assembly from 1941 until his death .
He was a member of the Labor Party and held numerous ministerial positions.
He was educated to elementary level at state schools and initially worked as a butcher.
He defeated the sitting Country Party member, Matthew Kilpatrick in the landslide victory that allowed William McKell to form a government.
During the premierships of McKell, James McGirr and Joseph Cahill, Graham held various ministerial portfolios, most notably his long tenure as Minister for Agriculture.