基于信息几何的网络复杂性量化
Quantifying Networks Complexity from Information Geometry Viewpoint
摘要：
考虑一个参数空间由随机变量方差给定的高斯统计模型。在这个模型的基础上，我们通过将随机变量解释为位于顶点上，并将它们的相关性解释为顶点之间的加权边来识别网络。然后，我们关联到参数空间的统计流形赋予黎曼度量结构（费舍尔-饶）。接着，类比于统计力学中熵的微正则定义，我们引入了网络复杂性的熵测度。我们证明了它在网络同构下是不变的。最重要的是，考虑到网络作为单纯复形，我们评估这个熵的单纯形，并发现它单调增加的尺寸。
英文摘要：
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy on simplexes and find that it monotonically increases with their dimension.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
