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Friday, October 13, 2017 - 09:30 to 10:30
SMS Seminar Room
Antar Bandyopadhyay
Indian Statistical Institute, New Delhi
De-Preferential Attachment Random Graphs

Abstract: In this talk we will introduce a new model of a growing sequence of random graphs where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied model of preferential attachment random graphs where higher degree vertices are preferred, we will call our model de-preferential attachment random graph model. We will consider two types of de-preferential attachment models, namely, inverse de-preferential, where the attachment probabilities are inversely proportional to the degree and linear de-preferential, where the attachment probabilities are proportional to $c-$degree, where $c > 0$ is a constant. We will give asymptotic degree distribution for both the model and show that the limiting degree distribution has very thin tail. We will also show that for a fixed vertex $v$, the degree grows as $\sqrt{\log n}$ for the inverse de-preferential case and as $\log n$ for the linear case, for a graph with $n$ vertices. Some of the results will also be generalized when each new vertex joins to $m > 1$ existing vertices.

[This is a joint work with Subhabrata Sen]

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