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The preferential attachment model

By Winfried Just1, Hannah Lea Callender2, Drew LaMar3, Ying Xin4

1. Department of Mathematics, Ohio University 2. University of Portland 3. College of William and Mary 4. Ohio University

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Abstract

Many empirically studied networks have approximately so-called power-law or scale-free degree distributions. In Section 1 we formally define such distributions and explore some of their properties. We also introduce and briefly compare two methods for constructing random networks with approximately power-law degree distributions: generic scale-free networks and the preferential attachment model. In Sections 2 and 3 we explore disease transmission on networks that are obtained from the preferential attachment model and implications for designing effective vaccination strategies.

Level: Advanced undergraduate students of biology or mathematics.

Requires: This module is fairly self-contained. Subsection 1.1 as well as Sections 2 and 3 require only basic familiarity with network models of disease transmission and IONTW to the extent covered in Module A quick tour of IONTW. Subsections 1.2 and 1.3 reference the construction given in Section 2 of Module Exploring contact patterns between two subpopulations.

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Cite this work

Researchers should cite this work as follows:

  • Winfried Just; Hannah Lea Callender; Drew LaMar; Ying Xin (2015), "The preferential attachment model," https://qubeshub.org/resources/384.

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