学位(音乐)
学位分布
不相关
缩放比例
节点(物理)
组合数学
随机图
分布(数学)
无标度网络
物理
离散数学
简并能级
统计物理学
数学
复杂网络
量子力学
统计
图形
数学分析
几何学
声学
出处
期刊:Physical review
日期:2003-04-25
卷期号:67 (4)
被引量:86
标识
DOI:10.1103/physreve.67.046118
摘要
We define a statistical ensemble of nondegenerate graphs, i.e., graphs without multiple-connections and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier publication [Phys. Rev. 64, 046118 (2001)] where trees and degenerate graphs were considered. An efficient algorithm generating nondegenerate graphs is constructed. The corresponding computer code is available on request. Finite-size effects in scale-free graphs, i.e., those where the tail of the degree distribution falls like n(-beta), are carefully studied. We find that in the absence of dynamical internode correlations the degree distribution is cut at a degree value scaling like N(gamma), with gamma=min[1/2,1/(beta-1)], where N is the total number of nodes. The consequence is that, independently of any specific model, the internode correlations seem to be a necessary ingredient of the physics of scale-free networks observed in nature.
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