The Annals of Applied Probability

Twitter event networks and the Superstar model

Shankar Bhamidi, J. Michael Steele, and Tauhid Zaman

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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.

Article information

Ann. Appl. Probab., Volume 25, Number 5 (2015), 2462-2502.

Received: November 2012
Revised: July 2014
First available in Project Euclid: 30 July 2015

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 05C80: Random graphs [See also 60B20] 90B15: Network models, stochastic

Dynamic networks preferential attachment continuous time branching processes characteristics of branching processes multitype branching processes Twitter social networks retweet graph


Bhamidi, Shankar; Steele, J. Michael; Zaman, Tauhid. Twitter event networks and the Superstar model. Ann. Appl. Probab. 25 (2015), no. 5, 2462--2502. doi:10.1214/14-AAP1053.

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