I dont understand what "graduated compression" means. Does it squish your toes and forefoot more tightly than your ankle and calf? Or vice versa? Or does it squish you progressively harder as the day progresses and your feet get more swollen? And, how much is the compression? Is it just basically a moderately stretchy sock, or is it powerful compression like squeezing your bottom into bicycle shorts?
Graduated compression socks squeeze your ankle. The squeezing feeling will decrease as the sock travels up your leg. The sock should be stretchy enough because of this.
Graduated compression socks have the greatest amount of pressure at the ankle with that compression level gradually decreasing towards the top and toes of the sock. While Carhartt doesn't grade their level of compression, the socks are fairly stretchy and not too strong of compression, as they only contain 1% Lycra.