Proper interval graphs are interval graphs that have an interval representation in which no interval properly contains any other interval; unit interval graphs are the interval graphs that have an interval representation in which each interval has unit length. A unit interval representation without repeated intervals is necessarily a proper interval representation. Not every proper interval representation is a unit interval representation, but every proper interval graph is a unit interval graph, and vice versa. Every proper interval graph is a claw-free graph; conversely, the proper interval graphs are exactly the claw-free interval graphs. However, there exist claw-free graphs that are not interval graphs.