A Gap in the Community-Size Distribution of a Large-Scale Social Networking Site

TL;DR

This paper analyzes a large-scale social networking site, revealing a community-size gap unexplained by existing models, and proposes a simple two-process model to account for various network properties.

Contribution

It introduces a novel community-size gap in SNSs and presents a simple two-process model that explains this feature along with other network statistics.

Findings

Identified a community-size gap in SNSs not explained by previous models.

Proposed a two-process model that reproduces the community-size gap and other network properties.

Model estimates the relative frequencies of acquaintance processes in social networks.

Abstract

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.