The genealogies of Greek mythology have been important for transforming the skeleton of disconnected myths into a flowing narrative with fully-developed characters. Without a full understanding of the inter-relationships it would have been impossible to understand the chronology of the myths, particularly in the context of the Trojan War. Furthermore on some occasions the genealogies challenged the standard chronology as mapped out by the ancient Greek commentators themselves, as I have discussed in greater detail elsewhere on this site
From an investigation of the family tree of Cheiron, the plot of the first book evolved significantly, drawing in the characters of Aeacus, Peleus and Telamon. Genealogies of the other kingdoms of ancient Greece introduced apparently incidental characters like Aegeus, Theseus and Minos, characters who will become more significant later in the saga. Other genealogies, like the houses of Thebes and Sparta, are used to augment the thread of the novels and tie it into the major myths of Oedipus, the Seven Against Thebes expedition and the Trojan War.
But in addition to forming the ligaments binding together the characters and myths of ancient Greece, the genealogies offer insight into potential motivations for actions by allowing the author to understand the background to the characters' lives and mischievously prefigure future events. I must admit to having done this with Odysseus' father Laertes and the depiction of Creon, Eteocles and Polyneices during Jason's visit to Thebes.
I will not attempt to recreate the excellent work of other researchers in including relevant genealogies on this site. At appropriate places on this site I will include links to relevant genealogies, but there are some links to external sites available on the right.