Persistence homology of networks: methods and applications

Applied Network Science

Table 2 The comparison of algorithms and applications on Single Graph

Paper	Filtration	Topological summary	Data
Benzekry et al. (2015)	Power filtration (POW) section	0-1 dim Betti numbers	PPI networks
Sizemore et al. (2018)	Vietoris-Rips filtration (VR) section	1-2 dim PD	Brain networks
Chung et al. (2013)	Vietoris-Rips filtration (VR) section	0 dim PD	Brain networks
Giusti et al. (2016)	Weighted simplex filtration (WS) section	0-2 dim PD	Brain Networks
Khalid et al. (2014)	Vietoris-Rips filtration (VR) section	0-dim PD	Brain Networks
Ignacio and Darcy (2019)	Vietoris-Rips filtration (VR) section	0-2 dim PD	Migration and remittance networks
Rucco et al. (2016)	Vietoris-Rips filtration (VR) section	1 dim PB	Simulated idiotypic networks
Salnikov et al. (2018)	Temporal filtration (TMP) section	1-2 dim PD	Co-occurrence networks
Suh et al. (2017)	Power filtration (POW) section	0 dim PB	Co-occurrence networks
Rieck et al. (2018)	Vertex-based clique filtration (VBCL) section, k-clique filtration (kCL) section	0 dim PD	Co-occurrence, brain and collaboration network