@article{guerra_homological_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.}, author = {Guerra, Marco and De Gregorio, Alessandro and Fugacci, Ulderico and Petri, Giovanni and Vaccarino, Francesco}, date = {2021-01-01}, eprint = {2004.11606}, eprinttype = {arxiv}, journaltitle = {{arXiv}:2004.11606 [cs, math, q-bio]}, keywords = {1 - Connectome, 1 - Quantitative Biology, 2 - Homological scaffolds, 2 - Network, 3 - Correlation matrix, 3 - Networks, 3 - Neuronal network, 3 - {fMRI}}, title = {Homological Scaffold via Minimal Homology Bases}, url = {http://arxiv.org/abs/2004.11606}, urldate = {2021-01-05} }