The war came to an end on 11 November 1918 where, just under two weeks before, Graham's first son, Mungo Alan Douglas, was born on 29 October. Graham relinquished his appointment as brigade major on 8 June 1919, and returned to regimental duty on 11 January 1920. From 30 October 1921 he was seconded to the Indian Army as an assistant military secretary. He returned to the United Kingdom and attended the Staff College, Camberley from 1924 to 1925 where, among his many fellow students there were Noel Irwin, Daril Watson, Ivor Thomas, Clifford Malden, Cyril Durnford, Michael Creagh, Thomas Riddell-Webster, James Harter, Sydney Wason, Langley Browning, Frederick Hyland, Otto Lund, Rufus Laurie, Gerald Fitzgerald, Arthur Barstow, John Reeve, Vyvyan Pope, Robert Studdert, Noel Napier-Clavering, Reade Godwin-Austen, Gerald Brunskill, Archibald Nye, George Lammie, Noel Beresford-Peirse, Gerald Gartlan, Geoffrey Raikes, Humfrey Gale, Guy Robinson and Lionel Finch. All of these men would, like Graham, become general officers in the future. He was then appointed a staff officer with the 52nd (Lowland) Infantry Division, a Territorial Army (TA) formation, from 19 February 1928.