On a geometrization of the Chung-Lu model for complex networks
On a geometrization of the Chung-Lu model for complex networks
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复杂网络Chung-Lu模型的几何化
DOI：
10.1093/comnet/cnu049
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
N. Fountoulakis
中科院分区：
文献类型：
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作者：
N. Fountoulakis
我们考虑由Krioukov等人引入的复杂网络模型，其中网络的内在层次被映射到双曲平面。Krioukov等人表明，该模型呈现聚类，其度的分布具有幂律尾巴。我们渐近地证明了该模型的局部行为类似于著名的Chung-Lu模型，其中两个节点独立连接，其概率与一些预先分配的权重的乘积成正比，其分布遵循幂律。利用这一方法，我们进一步准确地确定了任意顶点度的渐近分布。关键词：复杂网络数学分析，双曲几何，度分布
We consider a model for complex networks that was introduced by Krioukov et al. [14], where the intrinsic hierarchies of a network are mapped into the hyperbolic plane. Krioukov et al. show that this model exhibits clustering and the distribution of its degrees has a power law tail. We show that asymptotically this model locally behaves like the well-known Chung-Lu model in which two nodes are joined independently with probability proportional to the product of some pre-assigned weights whose distribution follows a power law. Using this, we further determine exactly the asymptotic distribution of the degree of an arbitrary vertex. keywords: mathematical analysis of complex networks, hyperbolic geometry, degree distribution