Any physical system can be viewed from the perspective that information is
implicitly represented in its state. However, the quantification of this
information when it comes to complex networks has remained largely elusive. In
this work, we use techniques inspired by quantum statistical mechanics to
define an entropy measure for complex networks and to develop a set of
information-theoretic tools, based on network spectral properties, such as
Renyi q-entropy, generalized Kullback-Leibler and Jensen-Shannon divergences,
the latter allowing us to define a natural distance measure between complex
networks. First we show that by minimizing the Kullback-Leibler divergence
between an observed network and a parametric network model, inference of model
parameter(s) by means of maximum-likelihood estimation can be achieved and
model selection can be performed appropriate information criteria. Second, we
show that the information-theoretic metric quantifies the distance between
pairs of networks and we can use it, for instance, to cluster the layers of a
multilayer system. By applying this framework to networks corresponding to
sites of the human microbiome, we perform hierarchical cluster analysis and
recover with high accuracy existing community-based associations. Our results
imply that spectral based statistical inference in complex networks results in
demonstrably superior performance as well as a conceptual backbone, filling a
gap towards a network information theory.

本文运用量子统计力学的技术来定义复杂网络的熵度量，并开发了一组基于网络谱属性的信息理论工具，可以用于最大似然估计和模型选择。通过将这个框架应用于人体微生物组的网络，我们通过层次聚类分析高精度地恢复出现有的社区关联。