By analyzing large networks, some interesting theories and applications have emerged.
The friendship paradox is one of the statistical paradoxes that frequently emerges in large networks.
This article from the NY times website describes this phenomena in quite some detail. This quote shows the general idea of the friendship paradox:
For any network where some people have more friends than others, it’s a theorem that the average number of friends of friends is always greater than the average number of friends of individuals.
Dunbar’s Number is another phenomena, extracted from applied evolutionary studies. Dunbar began formulating these ideas long before the internet and social networks became popular. HE looked at various civilization’s from differently sized groups of people throughout history, eventually postulating the average size of groups/communities to be around 100 – 230 (averagely around 150)
Dunbar also looked at the habits of Christmas cards being delivered in and around London, in order to calculate the networks that emerged and track the sizes and characteristics of modern communities. Read more here
These theories are only a few interesting things that can be seen or calculated through network science and social network analysis!