Random networks with concave preferential attachment rule

Reference:

Dereich, S. and Morters, P., 2011. Random networks with concave preferential attachment rule. Jahresberichte der Deutschen Mathematiker Vereinigung, 113 (1), pp. 21-40.

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Abstract

Many of the phenomena in the complex world in which we live have a rough description as a large network of interacting components. Random network theory tries to describe the global structure of such networks from basic local prin- ciples. One such principle is the preferential attachment paradigm which suggests that networks are built by adding nodes and links successively, in such a way that new nodes prefer to be connected to existing nodes if they have a high degree. Our research gives the first comprehensive and mathematically rigorous treatment of the case when this preference follows a nonlinear, or more precisely concave, rule. We survey results obtained so far and some ongoing developments.

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