作为真实网络代理或零模型的定制图集合I：结构量化工具
Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure.
作者信息
Annibale A, Coolen Acc, Fernandes Lp, Fraternali F, Kleinjung J
机构信息
Department of Mathematics, King's College London, The Strand, London WC2R 2LS, United Kingdom.
出版信息
J Phys A Math Gen. 2009 Dec 4;42(48). doi: 10.1088/1751-8113/42/48/485001.
Abstract
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.
摘要
我们研究如何将结构化随机图系综定制为真实网络，目的是生成精确且实用的数学工具，以便在宏观层面上量化和比较网络拓扑结构，超越度统计的范畴。我们的系综族可以生成具有任何规定度分布和任何度-度相关函数的图，其控制参数可以完全通过解析方法计算得出，因此我们可以（渐近地）计算熵、复杂度以及网络之间信息论距离的公式，这些公式直接且明确地以测量得到的度分布和度相关性来表示。
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