Before we get started, a recent article about Troy: https://www.smithsonianmag.com/history/in-search-of-troy-180979553/

Hospitality, aka 'Xenia'


Odysseus & Polyphemus | Pseudo-Chalcidic black figure vase painting
vase painting in British Museum, c. 530BCE
https://www.theoi.com/Gallery/L8.3.html

 In his mind Telemachus saw his father
coming from somewhere, scattering the suitors,
and gaining back his honor, and control
of all his property. WIth this in his mind,
he was the first to see Athena there.
He disapproved of leaving strangers stranded,
so he went straight to meet her at the gate,
and shook her hand, and took her spear of bronze,
and let his words fly out to her.
"Good evening,
stranger, and welcome. Be our guest, come share
our dinner, and then tell us what you need."
He led her in, and Pallas followed him.
Inside the high-roofed hall, he set her spear
beside a pillar in a polished stand,
in which Odysseus kept stores of weapons.
And then he led her to a chair and spread
a smooth embroidered cloth across the seat,
and pulled a footstool up to it. He sad
beside her on a chair of inlaid wood,...
...
Once they were satisfied with food and drink,
the suitors turned their mind to other things--
singing and dancing, glories of the feast.
A slave brought out a well-tuned lyre and gave it
to Phemius, the man the suitors forced
to sing for them. He struck the chords to start
his lovely song.
    Telemachus leaned in
close to Athena, so they would not hear,
and said,
"Dear guest--excuse my saying this--
these men are only interested in music--
a life of ease. They make no contribution.
This food belongs to someone else, a man
whose white bones may be lying in the rain...
...
Who are you? From what city and what parents?
WHat kind of ship did you arrive here on?
What sailors brought you here, and by what route?
You surely did not travel here on foot!
Here is the thing I really want to know:
have you been here before? Are you a friend
who visited my father? Many men
came to his house. He traveled many places."
Athena's clear bright eyes met his She said,
"Yes, I will tell you everything. Iam
Mentes, the son of wise Anchialus,
lord of the Taphians, who love the oar.
I traveled with my ship and my companions
over the wine dark sea to foreign lands,
with iron that I hopeto trade for copper
in Temese. My ship is in the harbor
far from the town, beneath the woody hill.
And you and I are guest-friends though our fathers,
from long ago--Laertes can confirm it.
...
Tell me now--are you
Odysseus' son? You are so tall!
Your handsome face and eyes resemble his.
We often met and knew each other well,
before he went to Troy...
...
Telemachus was careful as he answered.
"Dear guest, I will be frank with you. My mother
says that I am his son, but I cannot
be sure, since no one knows his own begetting.
I wish I were the son of someone lucky,
who could grow old at home with all his wealth.
Instead, the most unlucky man alive
is said to be my father--since you ask."
...
(Athena speaks) "May Odysseus
come meet the suitors with that urge to kill!
A bitter courtship and a short life for them!
But whether he comes home to take revenge
or not, is with the gods. You must consider
how best to drive these suitors from your house."
(she advises him to call an assembly and go search for news of his father)
if you hear that he
is dead, go home, and build a tomb for him,
and hold a lavish funeral to show
the honor he deserves, and give your mother
in marriage to a man. When this is done,
cosider deeply how you might be able
to kill the suitors in your halls--by tricks
or openly.... (cf. Telemachus' words at 375-80)

NOTE: Of course, such customs are not unique to Greece: they occur across the world. But the specifics of the type scenes in Homer, the language, and the particular objects offered make this particular institution of hospitality Homeric.

Related to this is a bigger question about the status of people versus things in Homer.
At least one scholar, Mary Scott, has plausibly suggested that the value of people is entirely instrumental in Homer. People are means to ends, not really any differently than the way possessions are means to ends, the end being preservation of honor, status, and survival. The idea that a person is and end in herself is not present in the epics. Some among later Greeks will theorize that a friend is "another self" and so should be of value in and of herself, but that doesn't seem to be the case in the epics.    


Of interest, but unrelated to guest-friendship, is this vase painting of Elpenor, Hermes, and Odysseus


Figure 3. A landscape “of unusual, even startling interest.” Red-figure pelikē: drawing of Side A, Odysseus, Elpenor, and Hermes in the Underworld. The Lykaon Painter, ca. 440 BCE. The Museum of Fine Arts, Boston, William Amory Gardner Fund, inv. no. 34.79.
https://archive.chs.harvard.edu/CHS/article/display/5722.chapter-2-greece-and-the-garden