Xiao Yanghua, Xiong Momiao, Wang Wei, Wang Hui
Department of Computing and Information Technology, Fudan University, Shanghai 200433, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 2):066108. doi: 10.1103/PhysRevE.77.066108. Epub 2008 Jun 11.
Many real networks have been found to have a rich degree of symmetry, which is a universal structural property of complex networks, yet has been rarely studied so far. One of the fascinating problems related to symmetry is exploration of the origin of symmetry in real networks. For this purpose, we summarized the statistics of local symmetric motifs that contribute to local symmetry of networks. Analysis of these statistics shows that the symmetry of complex networks is a consequence of similar linkage pattern, which means that vertices with similar degrees tend to share common neighbors. An improved version of the Barabaśi-Albert model integrating similar linkage pattern successfully reproduces the symmetry of real networks, indicating that similar linkage pattern is the underlying ingredient that is responsible for the emergence of symmetry in complex networks.
许多实际网络已被发现具有丰富的对称性，这是复杂网络的一种普遍结构特性，但迄今为止很少被研究。与对称性相关的一个引人入胜的问题是探索实际网络中对称性的起源。为此，我们总结了有助于网络局部对称性的局部对称基序的统计数据。对这些统计数据的分析表明，复杂网络的对称性是相似连接模式的结果，这意味着具有相似度数的顶点倾向于共享共同的邻居。整合了相似连接模式的巴拉巴西 - 阿尔伯特模型的改进版本成功地再现了实际网络的对称性，表明相似连接模式是负责复杂网络中对称性出现的潜在因素。
