Geometric protean graphs

TL;DR

This paper introduces the GEO-P model for online social networks, capturing key properties like power law degree distribution and small-world behavior, and proposes a new dimension measure to analyze user grouping based on link structure.

Contribution

The paper presents the GEO-P model that reflects real OSN properties and introduces a new network dimension for analyzing user similarity using only link data.

Findings

GEO-P model reproduces observed OSN properties

The model's dimension correlates with actual user attributes

Potential for user grouping based on link structure

Abstract

We study the link structure of on-line social networks (OSNs), and introduce a new model for such networks which may help infer their hidden underlying reality. In the geo-protean (GEO-P) model for OSNs nodes are identified with points in Euclidean space, and edges are stochastically generated by a mixture of the relative distance of nodes and a ranking function. With high probability, the GEO-P model generates graphs satisfying many observed properties of OSNs, such as power law degree distributions, the small world property, densification power law, and bad spectral expansion. We introduce the dimension of an OSN based on our model, and examine this new parameter using actual OSN data. We discuss how the geo-protean model may eventually be used as a tool to group users with similar attributes using only the link structure of the network.