Emergence of symmetry in complex networks.

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.