Growth of common friends in a preferential attachment model

The number of common friends (or connections) in a graph is a commonly used measure of proximity between two nodes. Such measures are used in link prediction algorithms and recommendation systems in large online social networks. We obtain the rate of growth of the number of common friends in a linea...

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Bibliographic Details
Published in:Stochastic models 2021-07, Vol.37 (3), p.427-447
Main Authors: Das, Bikramjit, Ghosh, Souvik
Format: Article
Language:English
Subjects:
Algorithms
Heavy-tail
limit theorem
link prediction
Phase transitions
preferential attachment
Primary 60F15
Recommender systems
Secondary 90B15
social network
Social networks
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Summary:The number of common friends (or connections) in a graph is a commonly used measure of proximity between two nodes. Such measures are used in link prediction algorithms and recommendation systems in large online social networks. We obtain the rate of growth of the number of common friends in a linear preferential attachment model. We apply our result to develop an estimate for the number of common friends that can significantly reduce the cost of computing these measures. We also observe a phase transition in the limiting behavior of the number of common friends; depending on the range of the parameters of the model, the growth is either power-law, or, logarithmic, or static with the size of the graph.
ISSN:1532-6349
1532-4214
DOI:10.1080/15326349.2021.1910521