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Title: Scale-free networks which are highly assortative but not small world
Authors: Small, M
Xu, X
Zhou, J
Zhang, J
Sun, J
Lu, JA
Keywords: Complex networks
Network theory (graphs)
Nonlinear dynamical systems
Issue Date: 20-Jun-2008
Publisher: American Physical Society
Source: Physical review E, statistical, nonlinear, and soft matter physics, June 2008, v. 77, no. 6, 066112, p. 1-7 How to cite?
Journal: Physical review E, statistical, nonlinear, and soft matter physics 
Abstract: Uncorrelated scale-free networks are necessarily small world (and, in fact, smaller than small world). Nonetheless, for scale-free networks with correlated degree distribution this may not be the case. We describe a mechanism to generate highly assortative scale-free networks which are not small world. We show that it is possible to generate scale-free networks, with arbitrary degree exponent γ>1, such that the average distance between nodes in the network is large. To achieve this, nodes are not added to the network with preferential attachment. Instead, we greedily optimize the assortativity of the network. The network generation scheme is physically motivated, and we show that the recently observed global network of Avian Influenza outbreaks arises through a mechanism similar to what we present here. Simulations show that this network exhibits very similar physical characteristics (very high assortativity, clustering, and path length).
ISSN: 1539-3755 (print)
1550-2376 (online)
DOI: 10.1103/PhysRevE.77.066112
Rights: Physical Review E © 2008 The American Physical Society. The Journal's web site is located at
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