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Local assortativeness in scale-free networks

M. Piraveenan1,2, M. Prokopenko1 and A. Y. Zomaya2

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The level of assortative mixing of nodes in real-world networks gives important insights about the networks design and functionality, and has been analyzed in detail. However, this network-level measure conveys insufficient information about the local-level structure and motifs present in networks. We introduce a measure of local assortativeness that quantifies the level of assortative mixing for individual nodes in the context of the overall network. We show that such a measure, together with the resultant local assortativeness distributions for the network, is useful in analyzing network's robustness against targeted attacks. We also study local assortativeness in real-world networks, identifying different phases of network growth, showing that biological and social networks display markedly different local assortativeness distributions to technological networks, and discussing the implications to network design.


PACS

89.75.Da Systems obeying scaling laws

89.75.Fb Structures and organization in complex systems

89.75.Hc Networks and genealogical trees

Subjects

Statistical physics and nonlinear systems

Dates

Issue 2 (October 2008)

Received 4 July 2008, accepted for publication 3 September 2008

Published 26 September 2008



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