The mandarin guangxi encompasses a whole lot more than just your network. That would be considered a very bastardised translation, losing all the extra meanings such as good luck created by having that network, possibilities to fortune, a kind of karma, and more.
Karma aside, "having connections"/being "well-connected" is pretty much the equivalent in English. It's not bastardised at all; terms don't need to have the exact same cultural implications to be basically equivalent.
> all the extra meanings such as good luck created by having that network, possibilities to fortune, a kind of karma, and more.
In your 20s you might think of your network as people who you went to college with. In your 40s your network takes on a meaning much closer to what you have described. I don’t yet know what happens in your 60s.