In the first three books of Homer's Odyssey, are there any examples of parallelism?
First, you'll need to answer the question, "What is parallel to what?" Is what happens to Telemachus parallel to what happens to Odysseus? Is what happens to Agamemnon when he returned from the Trojan War parallel to what will happen to Odysseus when he returns from the Trojan War? Is what happened to Nestor or Menelaus on their respective returns from Troy parallel to what will happen to Odysseus on his return from Troy?
Yes, several parallels in the first three books do exist, but you'll need to ask yourself these sorts of questions to arrive at the answer. Like Odysseus, Agamemnon left a wife and son at home when he went off to war; unlike Odysseus, though, Agamemnon's wife was not faithful when tempted by another man.
But when the gods at last destined that Agamemnon should be destroyed, Aegisthus took the minstrel to a desert isle, and left him there as a gift for the birds of prey: and as he wished, and she wished, led her to his own house. (Odyssey 3; A.S. Kline translation)
When Agamemnon returned home, Aegisthus killed him; but Aegisthus was in turn killed by Agamemnon's son Orestes. Will Telemachus become a second Orestes and kill the suitors who tempt his mother? In Odyssey 1, Athene encourages Telemachus to become like Orestes:
...use heart and mind to plan how to kill the Suitors in your palace, openly or by guile: since it is not right for you to follow childish ways, being no more a child. Perhaps you have not heard what fame Orestes won among men, destroying his father’s murderer, cunning Aegisthus, for killing his noble father?
So, we find lots of parallels in the first three books of the Odyssey. Comparing Odysseus, Penelope, Telemachus, and the suitors with Agamemnon, Clytemnestra, Orestes, and Aegisthus should bring out some striking similarities and differences.