The Cyclops mentioned in Hesiod’s Theogony and Homer’s Odyssey were one-eyed giants who came from the god Uranus and goddess Gaia.
The most popular story about the Cyclops is told in the Odyssey. It is about the Cyclops Polyphemus, the son of the sea-god Poseidon. The story runs as follows: Odysseus and his men became trapped in a cave in which they were resting by Polyphemus. The Cyclops ate two men every day. Finally Odysseus and his remaining men blinded the Cyclops’ eye and fled. But in his rage, Polyphemus called upon his father, who brought upon Odysseus troubles all the way to his homeland, delaying his journey ten years.
So, were these Cyclopes a civilization? It depends on how you look at it. On one hand they lived separately in caves and had no connection with one another. But one the other hand they were sheepherders and blacksmiths, and had families. Who knows if they had some form of government? It is impossible to say without more information whether or not the Cyclopes were a civilization.