Twitter event networks and the Superstar model

TL;DR

This paper introduces a new mathematical model for Twitter networks that captures the condensation phenomenon where a superstar node dominates edges, providing better empirical fit than traditional models and analyzing network structure asymptotics.

Contribution

The paper develops a tractable model for social network condensation phenomena, with rigorous limit results and improved empirical fit over standard preferential attachment models.

Findings

Superstar node captures a positive fraction of edges.

Degree distribution exhibits a power law tail.

Asymptotic properties of network height and maximum degrees.

Abstract

Condensation phenomenon is often observed in social networks such as Twitter where one "superstar" vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail. We formulate a mathematically tractable model for this phenomenon that provides a better fit to empirical data than the standard preferential attachment model across an array of networks observed in Twitter. Using embeddings in an equivalent continuous time version of the process, and adapting techniques from the stable age-distribution theory of branching processes, we prove limit results for the proportion of edges that condense around the superstar, the degree distribution of the remaining vertices, maximal nonsuperstar degree asymptotics and height of these random trees in the large network limit.