复杂网络中对称性的涌现
Emergence of Symmetry in Complex Networks
摘要：
许多真实网络都具有丰富的对称度，这是复杂网络的一个非常重要的结构性质，但迄今为止却鲜有研究。而对称性从何而来还没有得到解释。为了探索网络对称性的机制，我们研究了某些局部对称模体的统计，如对称双李格和广义对称双李格，这有助于网络的局部对称性。我们发现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的节点倾向于共享相似的连接目标。引入相似连接模式的改进BA模型成功地再现了真实网络的对称性，表明相似连接模式是复杂网络中对称性产生的根本原因。
英文摘要：
Many real networks have been found to have a rich degree of symmetry, which is a very important structural property of complex network, yet has been rarely studied so far. And where does symmetry comes from has not been explained. To explore the mechanism underlying symmetry of the networks, we studied statistics of certain local symmetric motifs, such as symmetric bicliques and generalized symmetric bicliques, which contribute to local symmetry of networks. We found that symmetry of complex networks is a consequence of similar linkage pattern, which means that nodes with similar degree tend to share similar linkage targets. A improved version of BA model integrating similar linkage pattern successfully reproduces the symmetry of real networks, indicating that similar linkage pattern is the underlying ingredient that responsible for the emergence of the symmetry in complex networks.
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