[2] Graver is Lincoln City's all-time leading scorer,[3] and topped the poll as the club's supporters voted for their "100 League Legends".
[9] Playing alongside Leicester's record goalscorer Arthur Rowley, Graver scored in his first two games, but produced little more as the club failed to avoid relegation.
[12] In August 1957, expectation was that he would return again to Lincoln; terms were agreed between the clubs, but Boston United – where his brother Alf was already playing – made the player a better contract offer.
[13][14] Not only did Boston pay a Midland League record fee of £3,500 for Graver, they also signed Johnny Garvie from Carlisle United with the intention of reviving their previous goalscoring partnership.
[15] He remained with the club as they began their 1958 campaign in the Southern League, scoring at a goal a game, before returning to Lincoln City for his third spell.
However, injury restricted Garvie to five appearances, and although Graver's 16 goals made him leading scorer in 1962–63, and contributed to a fourth-place finish in the Midland Counties League and a Derbyshire Senior Cup-winner's medal, he was soon dropped to the reserves, where a broken ankle brought about his retirement as a player.
[4][18] The following year, to mark the centenary of the Professional Footballers' Association (PFA), supporters were asked to vote for their club's all-time favourite player; Graver was again the Lincoln City choice.