Xulvi-Brunet R, Pietsch W, Sokolov I M
Institut für Physik, Humboldt Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036119. doi: 10.1103/PhysRevE.68.036119. Epub 2003 Sep 22.
We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabási-Albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes. We point out that the Barabási-Albert model displays dissortative behavior with respect to the nodes' degrees, while the node-randomized network shows assortative mixing. These kinds of correlations are visualized by discussing the shell structure of the networks around an arbitrary node. In spite of different correlation behaviors, all three constructions exhibit similar percolation properties. This result for percolation is also detected for a network with finite second moment and its corresponding randomized models.
我们讨论了三种具有相同度分布但相关性属性不同的无标度网络相关模型。从基于增长和优先连接的巴拉巴西-阿尔伯特构建方法出发，我们讨论了另外两种网络，它们是在对该方法的链接或节点进行随机化时出现的。我们指出，巴拉巴西-阿尔伯特模型在节点度方面表现出异配行为，而节点随机化网络则显示出同配混合。通过讨论围绕任意节点的网络壳层结构，可以直观呈现出这类相关性。尽管相关性行为不同，但所有这三种构建方法都表现出相似的渗流特性。对于具有有限二阶矩的网络及其相应的随机化模型，也检测到了这种渗流结果。
