基于对称性的复杂网络结构熵
Symmetry based Structure Entropy of Complex Networks
摘要：
精确地量化网络系统的异质性或无序性在网络系统的行为和功能研究中是非常重要的。虽然许多基于度的熵已经被提出来衡量真实网络的异质性，但网络结构中隐含的异质性还不能精确量化。因此，我们提出了一种新的结构熵的自同构划分的基础上，精确量化的网络结构的异质性。极端情况的分析表明，基于自同构划分的熵比基于度的熵能更精确地量化网络的结构异质性。我们还总结了许多真实网络的对称性和异质性统计，发现真实网络在自同构划分的角度确实比在基于度的熵的测量下描述的更异质;并且结构异质性与真实网络的对称性强烈负相关。
英文摘要：
Precisely quantifying the heterogeneity or disorder of a network system is very important and desired in studies of behavior and function of the network system. Although many degree-based entropies have been proposed to measure the heterogeneity of real networks, heterogeneity implicated in the structure of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition to precisely quantify the structural heterogeneity of networks. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropy. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are indeed more heterogenous in the view of automorphism partition than what have been depicted under the measurement of degree based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks.
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