k-core organization of complex networks -: art. no. 040601
k-core organization of complex networks -: art. no. 040601
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DOI：
10.1103/physrevlett.96.040601
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发表时间：
2006-02-03
影响因子：
8.6
通讯作者：
Mendes, JFF
中科院分区：
文献类型：
--
作者：
Dorogovtsev, SN;Goltsev, AV;Mendes, JFF
我们解析地描述了随机损坏的不相关网络的体系结构作为一组连续封闭的子结构-k-核心。k-核心是顶点至少有k个互连的最大子图。我们发现k-核的结构，它们的大小，和它们的出生点-自举逾渗阈值。我们证明了在具有有限平均数z（2）的次近邻网络中，k-核的出现是一个混合相变。相反，如果z（2）发散，网络包含无限序列的k-核心，这些核心对随机损伤具有超鲁棒性。
We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures-k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birthpoints-the bootstrap percolation thresholds. We show that in networks with a finite mean number z(2) of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z(2) diverges, the networks contain an infinite sequence of k-cores which are ultrarobust against random damage.