  Social networking sites (SNS) have recently used by millions of people all
over the world. An SNS is a society on the Internet, where people communicate
and foster friendship with each other. We examine a nation-wide SNS (more than
six million users at present), mutually acknowledged friendship network with
third million people and nearly two million links. By employing a
community-extracting method developed by Newman and others, we found that there
exists a range of community-sizes in which only few communities are detected.
This novel feature cannot be explained by previous growth models of networks.
We present a simple model with two processes of acquaintance, connecting
nearest neighbors and random linkage. We show that the model can explain the
gap in the community-size distribution as well as other statistical properties
including long-tail degree distribution, high transitivity, its correlation
with degree, and degree-degree correlation. The model can estimate how the two
processes, which are ubiquitous in many social networks, are working with
relative frequencies in the SNS as well as other societies.
