网络冗余度的谱特征
Spectral Characteristics of Network Redundancy
摘要：
许多现实世界的复杂网络包含大量的结构冗余，其中多个顶点扮演相同的拓扑角色。这种冗余自然产生于形成和塑造许多现实世界系统的简单增长过程。由于结构上冗余的元素可以在不改变网络结构的情况下进行置换，因此可以通过检查网络自同构（对称）群来正式研究冗余。在这里，我们使用群论的方法来给出一个完整的描述谱签名的冗余无向网络。特别是，我们描述了如何网络的自同构群可用于直接关联特定的特征值和特征向量与特定的网络图案。
英文摘要：
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many real-world systems. Since structurally redundant elements may be permuted without altering network structure, redundancy may be formally investigated by examining network automorphism (symmetry) groups. Here, we use a group-theoretic approach to give a complete description of spectral signatures of redundancy in undirected networks. In particular, we describe how a network's automorphism group may be used to directly associate specific eigenvalues and eigenvectors with specific network motifs.
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