# IEEE Transactions on Network Science and Engineering

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

By Varun Jog and Po-Ling Loh

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.

## Editorials and Announcements

Announcements

• We are pleased to announce that Dapeng Oliver Wu, a professor in the Department of Electrical & Computer Engineering at the University of Florida, has been named the new 2017-2018 EIC for the IEEE Transactions on Network Science and Engineering.

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## Call for Papers

### Special Issue on Scalability and Privacy in Social Networks

Submission deadline: September 1, 2017. View PDF.

The growing popularity of Online Social Networks and their emerging applications attracted much attention from both academia and industry. Due to their nature, social networks are considered as sources of Big Data containing large amounts of privacy-sensitive information. A social network is frequently abstracted using a mathematical model such as a graph, which is usually very large, that can later be used as an input to other algorithms for further processing. Recent reports show that if the abstractions of social networks are not properly designed, a large amount of private information can be extracted from them. As the area of Data Science and related technologies are getting more mature, it is highly possible that what is considered a safe abstraction of social networks today, becomes unsafe tomorrow. Unfortunately, the problem of designing privacy-aware social network abstractions is very challenging. Generally speaking, this is because a change in input data forces a change in the structure of the algorithms which will process the input data. Such change can also affect the output of the algorithm. Certainly, the emerging Big Data analytic techniques, such as differential analysis, will bring more complexity to this already-conundrum-like problem. Most importantly, any solution to this problem has to be scalable. This special issue aims to provide a prime venue for researchers from both academia and industry to discuss about this impelling, but not well-understood, problem.