Volume 111, Number 4, August 2015
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||02 September 2015|
Analysis and perturbation of degree correlation in complex networks
1 Neuroscience Research Center, Changsha Medical University - Changsha 410219, China
2 Department of Anatomy, Histology and Embryology, Changsha Medical University - Changsha 410219, China
3 Department of Basic Medical Sciences, Changsha Medical University - Changsha 410219, China
4 Department of Physics, Xiangtan University - Xiangtan 411105, Hunan, China
5 Department of Computer Science, Changsha Medical University - Changsha 410219, China
6 College of Science, QiLu University of Technology - Jinan 250353, Shandong, China
Received: 12 May 2015
Accepted: 3 August 2015
Degree correlation is an important topological property common to many real-world networks such as the protein-protein interactions and the metabolic networks. In the letter, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof of the consistency for the statistical measures, and reveal the general linear relation in the degree correlation, which provides a simple and interesting perspective on the analysis of the degree correlation in complex networks. By using the general linear analysis, we investigate the perturbation of the degree correlation in complex networks caused by the simple structural variation such as the “rich club”. The results show that the assortativity of homogeneous networks such as the Erdős-Rényi graphs is easily strongly affected by the simple structural changes, while it has only a slight variation for heterogeneous networks with broad degree distribution such as the scale-free networks. Clearly, the homogeneous networks are more sensitive to the perturbation than the heterogeneous networks.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.Fb – Structures and organization in complex systems
© EPLA, 2015
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