随机无标度网络的聚类
Clustering of random scale-free networks
摘要：
我们推导了度分布指数为$2<γ<3$的构形模型生成的无标度随机图的聚类系数的有限尺寸依赖性。度异质性增加了网络中三角形的存在，甚至可以与许多真实网络中的三角形相比较，即使是非常大的网络。我们还发现，对于值的$γ\approx 2$，聚类几乎是大小无关的，并在同一时间，成为一个{ \it事实上}非自平均拓扑属性。这意味着即使对于非常大的网络大小，单个实例网络也不能代表整体。
英文摘要：
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<γ<3$. Degree heterogeneity increases the presence of triangles in the network up to levels that compare to those found in many real networks even for extremely large nets. We also find that for values of $γ\approx 2$, clustering is virtually size independent and, at the same time, becomes a {\it de facto} non self-averaging topological property. This implies that a single instance network is not representative of the ensemble even for very large network sizes.
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