Answer:
Loyalty, as defined in the Odyssey seems to be the constant devotion to someone, the hopefully longing of their return and victory.
Homer seems to value loyalty over many of the other human traits, as Eumaeus gets not only Homer’s famous “you” but his own book as well. The swineherd is not the only character that Homer uses to show loyalty, Penelope and Telemachus show unyielding faithfulness to Odysseus throughout the epic poem; as do many other characters even gods. Homer demonstrates the value he places on loyalty through the use of these characters with their devotion to Odysseus. Through the use of these characters Homer shows the value of loyalty by their loyalty to Odysseus.
Excerpt: When Telemachus first meets Odysseus, after being convinced it really is his father, he immediately agrees to help the man take revenge, doing everything as his father orders as if he had known the man all his life. (pg. 346; 270-288)