Analysis of Centrality in Sublinear Preferential Attachment Trees via the Crump-Mode-Jagers Branching Process

@article{Jog2017AnalysisOC,
  title={Analysis of Centrality in Sublinear Preferential Attachment Trees via the Crump-Mode-Jagers Branching Process},
  author={Varun S. Jog and Po-Ling Loh},
  journal={IEEE Transactions on Network Science and Engineering},
  year={2017},
  volume={4},
  pages={1-12}
}
We investigate centrality and root-inference properties in a class of growing random graphs known as sublinear preferential attachment trees. We show that a continuous time branching processes called the Crump-Mode-Jagers (CMJ) branching process is well-suited to analyze such random trees, and prove that almost surely, a unique terminal tree centroid emerges, having the property that it becomes more central than any other fixed vertex in the limit of the random growth process. Our result… CONTINUE READING

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Existence of a persistent hub in the convex preferential attachment model

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