He was taught to play cricket at Berwick Grammar School, by its owner/founder Edward Antonio Lloyd Vieusseux (1854–1917).

He was a resolute batsman, a distinct characteristic being the alteration of his style to suit varying conditions of wickets.

Graham was regarded as the best wet wicket batsman who ever played for Australia, whilst his equal as an outfield has rarely been seen.

After he retired from first-class cricket in Australia, in 1903 Graham accepted the post of coach at Otago Boys' High School in Dunedin.

[25] "In his later years Graham was gripped with alcoholism and mental illness and he was committed to an asylum near Dunedin, New Zealand in 1907 where he remained until his death".

When the "Little Dasher" blossomed out into an international player eighteen years ago, he was the cricket public's idol.