Line graphs as social networks

TL;DR

This paper explores the topological similarities between line graphs and social networks, suggesting that social networks can be modeled as line graphs of underlying community structures, supported by data from the LiveJournal network.

Contribution

It introduces a model where social networks are represented as line graphs of community-based networks, highlighting their clustering and assortativity features.

Findings

Line graphs exhibit clustering and assortativity similar to social networks.

Degree dependence of clustering coefficient shows maxima linked to cliques.

LiveJournal data supports the line graph model of social networks.

Abstract

The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8 x 10^6 people. In particular, sharp maxima of the observed data of the degree dependence of the clustering coefficient C(k) are associated with cliques in the social network.