How is hospitality an example of a Greek cultural value in The Odyssey?

The theme of hospitality occurs in numerous places. As Odysseus and his men are traveling, they must rely on the generosity of those whom they encounter, both gods and mortals alike. Sometimes they are not the best guests, such as when they disobediently eat the cattle of the sun god, Helios. At the other extreme, when the travelers meet Polyphemus, and Odysseus requests the culturally expected hospitality, the Cyclops decisively violates the norm: he eats some of Odysseus’s men.
The main place where hospitality figures prominently, however, is back home in Ithaca. Penelope must uphold her position as Odysseus's wife and keep a hospitable environment in their home. The suitors cluster around her, waiting for her to declare Odysseus dead and marry one of them. They test her patience with their bad behavior, which ranges from merely opportunistic to rude to homicidal. Penelope understands, however, that the honor of her and Odysseus’s family depends on her magnanimity. When their son, Telemachus, returns home from Troy, he loses his patience and starts to make the suitors feel unwelcome.
Hospitality is so crucial, in fact, that the entire resolution of the epic rests on it. Tired of waiting and concerned about Telemachus’s objections, several suitors conspire to kill him. Finally, when Odysseus himself returns disguised as a beggar, the suitors torment and attack him. Distressed that they dare to do this in her home, Penelope calls the beggar to an interview, thus beginning the process of reunion with her husband that will also result in him and Telemachus slaughtering all the suitors.