Hołyst Janusz A, Sienkiewicz Julian, Fronczak Agata, Fronczak Piotr, Suchecki Krzysztof
Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2 Pt 2):026108. doi: 10.1103/PhysRevE.72.026108. Epub 2005 Aug 8.
Universal scaling of distances between vertices of Erdos-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k(i) and k(j) equals to (l(ij)) = A - B log(k(i)k(j)). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree (k)nn calculated for the nearest neighbors and on network clustering coefficients.
人们观察到，在厄多斯-雷尼随机图、无标度巴拉巴西-阿尔伯特模型、科学合作网络、生物网络、互联网自治系统和公共交通网络中，顶点之间的距离存在普遍缩放现象。度为k(i)和k(j)的两个节点之间的平均距离等于(l(ij)) = A - B log(k(i)k(j))。这种缩放关系在几十年内都是有效的。本文提出了一个关于这种缩放现象出现的简单理论。参数A和B取决于为最近邻计算的节点度(k)nn的平均值以及网络聚类系数。
