Structure of a large social network

TL;DR

This paper analyzes a large social network, revealing complex degree distributions and clustering patterns, and introduces a new model that replicates these features, highlighting the coexistence of multiple network types in human social structures.

Contribution

The paper presents a novel growing random model based on local interactions that accurately reproduces observed scaling behaviors in large social networks.

Findings

Degree distribution has two power-law regimes separated by a critical degree.

Local clustering follows a power-law relation with degree.

The model successfully replicates all observed scaling features.

Abstract

We study a social network consisting of over $10^4$ individuals, with a degree distribution exhibiting two power scaling regimes separated by a critical degree $k_{\rm crit}$, and a power law relation between degree and local clustering. We introduce a growing random model based on a local interaction mechanism that reproduces all of the observed scaling features and their exponents. Our results lend strong support to the idea that several very different networks are simultenously present in the human social network, and these need to be taken into account for successful modeling.