title: Scale-free networks which are highly assortative but not small world.
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 gamma>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).
authors.affiliation: Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong. small@ieee.org
authors.forename: Michael
authors.initials: M
authors.lastname: Small
authors.forename: Xiaoke
authors.initials: X
authors.lastname: Xu
authors.forename: Jin
authors.initials: J
authors.lastname: Zhou
authors.forename: Jie
authors.initials: J
authors.lastname: Zhang
authors.forename: Junfeng
authors.initials: J
authors.lastname: Sun
authors.forename: Jun-An
authors.initials: JA
authors.lastname: Lu