Song H Francis, Wang Xiao-Jing
Center for Neural Science, New York University, New York, New York 10003, USA.
Center for Neural Science, New York University, New York, New York 10003, USA and NYU-ECNU Institute of Brain and Cognitive Science, NYU Shanghai, Shanghai, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Dec;90(6):062801. doi: 10.1103/PhysRevE.90.062801. Epub 2014 Dec 1.
Small-world networks-complex networks characterized by a combination of high clustering and short path lengths-are widely studied using the paradigmatic model of Watts and Strogatz (WS). Although the WS model is already quite minimal and intuitive, we describe an alternative formulation of the WS model in terms of a distance-dependent probability of connection that further simplifies, both practically and theoretically, the generation of directed and undirected WS-type small-world networks. In addition to highlighting an essential feature of the WS model that has previously been overlooked, namely the equivalence to a simple distance-dependent model, this alternative formulation makes it possible to derive exact expressions for quantities such as the degree and motif distributions and global clustering coefficient for both directed and undirected networks in terms of model parameters.
小世界网络——以高聚类和短路径长度相结合为特征的复杂网络——使用瓦茨和斯特罗加茨（WS）的范式模型进行了广泛研究。尽管WS模型已经相当简洁直观，但我们描述了一种WS模型的替代形式，它基于距离相关的连接概率，在实际和理论上都进一步简化了有向和无向WS型小世界网络的生成。除了突出WS模型一个先前被忽视的基本特征，即与一个简单的距离相关模型的等效性之外，这种替代形式还使得能够根据模型参数得出有向和无向网络的度分布、 motif分布和全局聚类系数等数量的精确表达式。
