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.

Homological scaffold via minimal homology bases / Guerra, Marco; De Gregorio, Alessandro; Fugacci, Ulderico; Petri, Giovanni; Vaccarino, Francesco. - In: SCIENTIFIC REPORTS. - ISSN 2045-2322. - ELETTRONICO. - 11:1(2021), p. 5355. [10.1038/s41598-021-84486-1]

Homological scaffold via minimal homology bases

Guerra, Marco;De Gregorio, Alessandro;Vaccarino, Francesco
2021

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2876060