Introversion often comes from social super powers. Introverts can be more sensitive and pick up on social cues from others more readily. I consider myself a "social introvert" this way - relationships are important, but I can be easily overwhelmed, and need a break. For many introverts, they are just as social, they just have to pace themselves.

I network by going deep rather than broad in my relationships. I don't worry about the quantity, but the quality. Over time, this snowballs where I develop a rich network gradually over time.

I observe a lot of extroverts can develop many superficial relationships that decay quickly... So I'd actually ask the opposite question, how to extroverts build a robust network? :-p