 He was a regular for Arsenal's first three seasons after the war (from 1919 until 1922), but the arrival of Jack Butler meant Graham had competition for his place and at the start of 1922–23 he lost his regular centre half berth, though he continued to be used as a bit-part player deputising in other half-back positions for that season and the next one.He played 179 times for Arsenal in total, scoring 20 goals (many of them penalties) and departed Highbury in December 1924.Graham joined Third Division South club Brentford in December 1924 for a £450 fee.