I had the great good fortune to see Davy Graham play live in the back room at Andy's Guitar Shop in London in 1993 in front of perhaps 50 people (the space is similar to McCabe's guitar shop in Santa Monica). It was the only time I've ever been to London, and it was one of the rare occasions on which he played during that period. At age 53 he still retained most of his amazing skill.
He held the guitar in an unusual position: With the body of the guitar held in his lap, and the neck held very high, not quite vertical, but nearly so. The dexterity of his fingers was astonishing: It seemed as if the guitar strings were each an inch apart, he played so effortlessly. There was nothing close to a wrong note: The sound of each string was crystal clear, and exactly on pitch. He played everything from folk to jazz to classical. At the end of the show, as was apparently customary, amateur guitarists in the audience came on stage to play, and he gave advice, like a master class. Truly a magical evening.
Those who were influenced by Davy Graham comprise a long long list: he invented the English folk-baroque movement (influencing everyone from John Renbourn and Bert Jansch on down); Paul Simon as mentioned above; Jimmy Page (the intro to Stairway to Heaven is a slowed down note for note copy of Davy's Cry Me a River, which can be viewed on YouTube); he arguably invented jazz-blues; he was the first to import Northern African, Middle Eastern and Indian rhythms into pop/rock music, which was subsequently copied by The Beatles, The Rolling Stones, et al.
There is a story that he went to a gathering of young English folkies in the early 60s. Renbourn and Jansch were there. After five minutes Jansch put his guitar down, and Renbourn five minutes later, and they just listened to Davy play, he was just in another league.
Fortunately his work was reissued on cd during the last 10 years of his life. What comes through is not only the wizardry of his playing (I don't know of any pop/rock/folk guitarist who can compare with him tehnically), but also his natural understanding of rhythm and phrasing. His guitar swings like no other. His cover of Art Blakey's Buhaina Chant on the Hat cd will blow you away.
His most recent cd, issued earlier this year, shows his technical skills in marked decline, but the musicianship of a lifetime still triumphs: The songs are played and sung with the rhythm and phrasing of an old soul, and are very very moving.
He was an original in every respect, good and bad. There will not be another like him.