Twitter event networks and the Superstar model
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Zaman_Twitter event.pdf
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Author(s)
Bhamidi, Shankar
Steele, J. Michael
Zaman, Tauhid R
Date Issued
July 2015
Journal
The Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Citation
Bhamidi, Shankar; Steele, J. Michael and Zaman, Tauhid. “Twitter Event Networks and the Superstar Model.” The Annals of Applied Probability 25, no. 5 (October 2015): 2462–2502 © 2015 Institute of Mathematical Statistics
Version
Final published version
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.
MIT Department
Sloan School of Management
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1214/14-aap1053
