Politecnico di Torino, Department of Mathematical Sciences, Torino, Italy.
CNR-IMATI, Genova, Italy.
Sci Rep. 2021 Mar 8;11(1):5355. doi: 10.1038/s41598-021-84486-1.
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.
同调支架利用持久同调来构建加权网络的拓扑结构良好的总结。然而，它对代表循环选择的关键依赖阻碍了将全局特征追溯到单个网络组件的能力，除非提供一种原则性的选择方法。在本文中，我们应用最近在最小同源基础计算方面的进展，引入了一种准规范版本的支架，称为最小支架，并将其应用于实际和模拟数据的分析。同时，我们验证了对于足够复杂的网络，标准支架在统计上是最小支架的良好代理。
