Small Michael, Xu Xiaoke, Zhou Jin, Zhang Jie, Sun Junfeng, Lu Jun-An
Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 2):066112. doi: 10.1103/PhysRevE.77.066112. Epub 2008 Jun 20.
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).
不相关的无标度网络必然是小世界网络（实际上，比小世界网络更小）。然而，对于具有相关度分布的无标度网络，情况可能并非如此。我们描述了一种生成非小世界的高度 assortative 无标度网络的机制。我们表明，有可能生成具有任意度指数γ>1 的无标度网络，使得网络中节点之间的平均距离很大。为了实现这一点，节点不是通过优先连接添加到网络中的。相反，我们贪婪地优化网络的 assortativity。网络生成方案有物理动机，并且我们表明最近观察到的禽流感爆发全球网络是通过与我们这里提出的类似机制产生的。模拟表明，这个网络表现出非常相似的物理特征（非常高的 assortativity、聚类和路径长度）。
