Placement in a network and access to networks absolutely does have a role in determining poverty/wealth.

I was born into an affluent community, and because of this I received a leg up over a male born on a fundamentalist-LDS compound in Texas, or an unschooled boy from Waziristan. I can leverage my network in my own self-interest to gain outsized value from my contacts, and any assistance I provide to my network will give me an outsized reward.

If I were connected largely to poor people, or powerless people, I would be less effective and have much weaker hopes when it comes to income.