+91-674-249-4082

Submitted by nabinjana on 5 September, 2017 - 17:37

Date/Time:

Friday, October 13, 2017 - 09:30 to 10:30

Venue:

SMS Seminar Room

Speaker:

Antar Bandyopadhyay

Affiliation:

Indian Statistical Institute, New Delhi

Title:

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.

**School of Mathematical Sciences**

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Tel: +91-674-249-4081

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