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Mark Newman

Print publication date: 2018

Print ISBN-13: 9780198805090

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198805090.001.0001

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Models of network formation

Models of network formation

(p.434) Chapter 13 Models of network formation

Mark Newman

Oxford University Press

This chapter describes models of the growth or formation of networks, with a particular focus on preferential attachment models. It starts with a discussion of the classic preferential attachment model for citation networks introduced by Price, including a complete derivation of the degree distribution in the limit of large network size. Subsequent sections introduce the Barabasi-Albert model and various generalized preferential attachment models, including models with addition or removal of extra nodes or edges and models with nonlinear preferential attachment. Also discussed are node copying models and models in which networks are formed by optimization processes, such as delivery networks or airline networks.

Keywords:   Generative model, preferential attachment, cumulative advantage, Matthew effect, Price model, citation network, Barabasi-Albert model, power law, scale-free network, first mover effect, nonlinear preferential attachment, node copying, network optimization, airline network, road network

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