Final answer:
The central theme of the House of Atreus is betrayal and revenge, indicated by the characters' cycle of violence and consequences that span generations.
Step-by-step explanation:
Betrayal and revenge. Within this narrative, the characters are heavily involved in a cycle of violence and retribution that impacts successive generations. The reference to the lineage being 'mixed' and the use of adultery to gain the throne speaks to the tangled web of deceit and betrayal that characterizes the theme. Atreus himself references a 'heavenly sire' sending him a sign which could imply divine intervention, but this is more a narrative device to justify his actions rather than a central theme.
The House of Atreus often serves as a cautionary tale about the destructive power of betrayal and the unending quest for revenge. The story warns of the consequences of such actions, showing how they ultimately lead to the downfall of even the most powerful families, affecting multiple generations and leaving a legacy of sorrow and ruin.