It seems to me that the Nostr protocol is simultaneously capitalist and socialist.

Everyone independently owns their social graph, and everyone collectively owns the network itself.

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That's not socialist. That's rough consensus. Rough consensus is public property that you can choose to privately opt out of, therefore not socialist.

Fair. I think it approaches the socialist utopian fantasy though

That's because information is magical. It can be transmitted and copied so easily it's almost a free good.

Can someone explain to me the social graph? I don't understand it.

Also how is the equivalent of my history stored on relays/nostr?

I’m definitely not the best person to ask but as I understand it, the social graph is just all of your content and following.