Exact bounds for degree centralization

被引:41
作者
Butts, Carter T. [1 ]
机构
[1] Univ Calif Irvine, Dept Sociol, Inst Math Behav Sci, Irvine, CA 92697 USA
基金
美国国家科学基金会;
关键词
degree centralization; density; graph order; graph level indices;
D O I
10.1016/j.socnet.2005.07.003
中图分类号
Q98 [人类学];
学科分类号
030303 ;
摘要
Degree centralization is a simple and widely used index of degree distribution concentration in social networks. Conventionally, the centralization score is normalized by the maximum value attainable at the observed order; this results in a measure on the unit interval. Here, exact bounds are provided for degree centralization given density as well as order. It is shown that roughly half of the region of conceivable degree centralization scores is actually feasible, and that the geometry of the feasible region alters with graph size. Concentration of the distribution of graphs within the feasible region is shown, and a renormalized family of degree centralization indices which adjusts for both density and order is provided. (c) 2005 Published by Elsevier B.V.
引用
收藏
页码:283 / 296
页数:14
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