Principled Network Skeletonization via Minimal Homology Bases
Guerra, Marco, De Gregorio, Alessandro, Petri, Giovanni and Vaccarino, Francesco (2021) Principled Network Skeletonization via Minimal Homology Bases. Scientific Reports.
Abstract
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.
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