It'd be nice to see how the different factions react to each other (which ones are friends and which ones attack each other on sight).

NCR:
Legion : Khans:
Boomers World

Chairmen World

Enclave NCR/Legion/House

Brotherhood of Steel:

Spoiler

Brotherhood of Steel NCR
Brotherhood of Steel Legion
Brotherhood of Steel House

House:

Spoiler

House Legion
House NCR
House Brotherhood of Steel
House Powder Gangers
House The Kings

Sorry for not putting a proper diagram up, but that is what I can remember at the moment.

(Note: some of this is not gameplay wise, but story/dialouge wise.)

A bit more:

Legion :Friendly/Hostile: Fiends (Unsure of which)

Khans :Friendly/hostile.neutral: Vault 19 Powder Gang.

Awesome! I'll build one myself out of what you've started me with.

I'm looking more for Gameplay than story. For example,

So basically I'm going off whatever two NPCs would do if they met in the wild.

I edited a few here that I thought would be different and included the Fiends and Powder Gangers (Vault 19)

In that case...

Enclave :Hostile/Friendly: NCR

Enclave :Friendly/Hostile: Legion