I think though there is an aspect that it is as much nurture as nature.
My parents are introverts. Other than relatives, and my Godmother, I think in my 20 years living at home we had one family stay over night for a visit, and I can tell you exactly where we'd stayed over (both grandparents, and my aunt).
Dm did have friends with children our age, and they came round, but it was planned.
We weren't allowed to run round the village the way the other children did (probably with fairly good reason!)
Having a friend back was a big deal.
Looking back, that suited my siblings. They're pretty antisocial. 
I think if I'd been allowed more social interactions on my own merit, then I probably would be more extrovert. I always felt honoured to be part of a friendship group, and thankful to be invited round because I felt it was an imposition, as my family tended to act as though it was.
And with my dc I have seen this too. The extrovert families tended to invite loads back. "Doesn't matter what the house looks like, we'll have some fun" and the children got used to having lots of people around.
I'm thinking of one couple I know. Mum extrovert, dad introvert and children (I've known them for years) a mixture. But even the introvert ones are fairly extrovert given the right situation, and I think it's because there were always loads of people around.
If I could do my time again with the children being small, it's one thing I'd change. I'd make sure there were children back every week (obviously not at the moment) and invite parents to come for coffee etc. I think that would have helped my dc find their feet socially much more.