In The Odyssey, what is the correlation of family members between Agamemnon’s family and Odysseus’ household?This is in book one.
The two families are of significant comparison throughout the epic. Zeus begins the story with his lament for the death of Agamemnon. We are told of Clytemnestra and Aegisthus plotting the death of Agamemnon before he returns from Troy. The story is then complete when Orestes (their son) avenges his father's death. Orestes gains a reputation for himself, just as his father had a wonderful reputation as a man and as a warrior.
It is then Telemachus' journey into maturation as well as his father's physical journey home that makes up The Odyssey. Telemachus must become a man just like Orestes did to help his father regain his kingdom. However, there is no lack of loyalty on Penelope's part. But Odysseus must test her all the same. He was warned by Agamemnon to check for her faithfulness.
Athena seeks Telemachus in Ithaca and tells him
. . . You should not go on clinging to your childhood. You are no longer of an age to do that. Or have you not heard what glory was won by great Orestes among all mankind, when he killed the murderer of his father, the treacherous Aigisthos, who had slain his famous father? So you too, dear friend, since I can see you are big and splendid, be bold also, so that in generations to come they will praise you.
Telemachus must then make his journey in order to aid his father in the end.