Many of the political, social and moral issues at play in the story of
the Odyssey can be summed up by considering two Greek terms: xenia
"hospitality" and oikos "household."
xenia: the law/custom of offering protection and hospitality to
strangers (cf. its opposite: xenophobia). The law/custom was felt
to be so fundamental to human civilized life that its patron was Zeus
xenios:"Zeus the god who protects strangers."
xenia is from the Indo-European root ghos-ti: 'a person
with whom the law of hospitality applies': this root is the source of a
number of English words that refer to outsiders, whether to be welcomed
or worried over: cf. hostile (Latin hostis, "enemy"),
"guest" (cf. hotel) "host" (cf. hospitality). Paris
violated xenia when he was a guest in Menelaus' house; Odysseus
searches for xenia in the sense of "hospitable reception" in a
wide variety of situations' in Bks. 9-12, as well as on Ithaca itself and
even in his own house.
oikos: a household based in land ("where one dwells," cf.
economy, ecology), whether of a noble or a common
The oikos includes not only the resident "family" in our sense of
the term but also all those who live in the house or its dependencies and
contribute to its wealth and survival: this may include slaves,
"illegitimate" children (often offspring of the master and slave women),
resident in-laws and "adopted" persons who serve as retainers or
Those who do not belong to a household (as Odysseus sometimes appears)
may be difficult to place: they could be valuable craftsmen who do not
themselves own land but serve those who do; or they could be vagabonds or
exiles, threatening instability.
The master of the oikos distributes tasks and goods among its
members and forms alliances with the masters of other oikoi
(plural). Thereby his house grows in wealth, strength and status measured
against other oikoi.
There is no strictly defined procedure for the succession of masters of oikoi, nor for the determination of which oikos in a community is the preeminent, the "kingly," one. Odysseus' father Laertes is still alive but has apparently laid this burden down. Odysseus' son may be the presumptive successor to his father as head the noblest house in Ithaca, but Telemachus will have to assert and defend this claim.
The suitors envision a situation in which Penelope, the queen, might marry one of them and move to his oikos, thus enobling as well as enriching it. This would leave Telemachus as head of his household but not with the kingship--i.e. leading the royal house of Ithaca.
See further the wonderful short book by M. I. Finley, The World of Odysseus (New York, 1978).