Gabel Alan, Krapivsky P L, Redner S
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):050802. doi: 10.1103/PhysRevE.88.050802. Epub 2013 Nov 12.
We introduce a class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the parent of the target with probability r, where r is an increasing function of the degree of the parent. This mechanism leads to highly dispersed networks with unusual properties: (i) existence of multiple macrohubs-nodes whose degree is a finite fraction of the total number of network nodes N, (ii) lack of self-averaging, and (iii) anomalous scaling, in which N(k), the number of nodes of degree k scales as N(k)~N(ν-1)/k(ν), with 1<ν<2.
我们引入了一类通过增强重定向来生长的网络。节点按顺序引入，每个节点以概率1 - r连接到随机选择的目标节点，或以概率r连接到目标节点的父节点，其中r是父节点度的增函数。这种机制导致具有异常特性的高度分散网络：（i）存在多个宏观枢纽节点，其度是网络节点总数N的有限分数；（ii）缺乏自平均性；（iii）异常标度，其中度为k的节点数N(k)按N(k)~N(ν - 1)/k(ν)标度，1 < ν < 2。
