Well, poor people definitely are more likely to be black, and black people are more likely to be poor. (In the US, which is the country OP is talking about, and in the UK, where I am, and in many other places, though maybe not everywhere.)

Being black tends, for obvious reasons, to run in families. So race-associated poverty will do so too. Some other factors that tend to go along with poverty run in families, some not. There is some tendency for people to associate with others of the same race, and some tendency for people to associate with others of similar social class. It's not obvious to me whether being black is a better or a worse predictor of having poor friends and families than being poor is.

> I don't see why race would affect this.

It does for lots of reasons.

> If you're poor, from a poor background, it's likely your friends are also poor, regardless of race.

If your even modestly successful and black from a poor background, it is more likely that you are the most successful person at a given network distance from people in your network than if you are equally successful and from an equally poor background but white. This is largely an effect of past racism.

But it's also less likely that people in your network can work their way up without your help. And that's largely a product of current racism, both of the institutional and the more direct, active, personal kind. (Also past racism, too.)