Rewatching Goblet of Fire, I wanted to see the whole web at once: Fawkes gave exactly two tail feathers. Ollivander put one in Harry's holly wand and one in Tom Riddle's yew wand, and that's why Priori Incantatem happens in the graveyard.

So I mapped it: Fawkes → the two feathers → the two wands → Harry and Voldemort, plus Dumbledore (Fawkes's owner), Ollivander, Lily, James and Snape around them.

Things that stood out once it was laid out:

• Dumbledore is linked to both wands through Fawkes, years before either boy got them
• The wands are "brothers", but their owners are linked only through Voldemort's choice to mark Harry
• Snape's whole arc hangs off one link: Lily

What connection did I miss?

Disclosure: I built the tool I made this in, Tree Tier. Happy to share the interactive version if anyone wants to click around.