Date of this Version
The Annals of Applied Probability
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.
The original and published work is available at: https://projecteuclid.org/euclid.aoap/1438261046#abstract
Dynamic networks, preferential attachment, continuous time branching processes, characteristics of branching processes, multitype branching processes, Twitter, social networks, retweet graph
Bhamidi, S., Steele, J. M., & Zaman, T. (2015). Twitter Event Networks and the Superstar Model. The Annals of Applied Probability, 25 (5), 2462-2502. http://dx.doi.org/10.1214/14-AAP1053
Date Posted: 27 November 2017
This document has been peer reviewed.