Analysis of centrality in sublinear preferential attachment trees via the CMJ branching process
2016
Online
report
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 generalizes and extends previous work establishing persistent centrality in uniform and linear preferential attachment trees. We also show that centrality may be utilized to generate a finite-sized $1-\epsilon$ confidence set for the root node, for any $\epsilon > 0$ in a certain subclass of sublinear preferential attachment trees.
Comment: 23 pages, 4 figures. An error in Lemma 15 in the earlier version has been fixed by modifying our theorems to establish terminal centrality. This paper has been accepted to IEEE Transactions on Network Science and Engineering
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Analysis of centrality in sublinear preferential attachment trees via the CMJ branching process
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Autor/in / Beteiligte Person: | Jog, Varun ; Loh, Po-Ling |
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Veröffentlichung: | 2016 |
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