Clustering coefficients of large networks
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- 作者：Yusheng Li ; Yilun Shang ; shylmath@hotmail.com ; shyl@tongji.edu.cn ; Yiting Yang
- 关键词：Clustering coefficient ; Theoretic graph ; Real-world network
- 刊名：Information Sciences
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：382-383
- 期：Complete
- 页码：350-358
- 全文大小：673 K
- 卷排序：382
文摘
Let G be a network with n nodes and eigenvalues λ1 ≥ λ2 ≥ ⋅⋅⋅ ≥ λn. Then G is called an (n, d, λ)-network if it is d -regular and λ=max{|λ2|,|λ3|,⋯,|λn|}λ=max{|λ2|,|λ3|,⋯,|λn|}. It is shown that if G is an (n, d, λ )-network and λ=O(d), the average clustering coefficient c¯(G) of G satisfies c¯(G)∼d/n for large d . We show that this description also holds for strongly regular graphs and Erdős–Rényi graphs. Although most real-world networks are not constructed theoretically, we find that many of them have c¯(G) close to d¯/n and many close to 1−μ2¯(n−d¯−1)d¯(d¯−1), where d¯ is the average degree of G and μ2¯ is the average of the numbers of common neighbors over all non-adjacent pairs of nodes.