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Table 3 The comparison of algorithms and applications on Multiple Graphs

From: Persistence homology of networks: methods and applications

Paper Filtration Topological Summary Data
(Chowdhury and Mémoli 2016; 2018) Dowker sink and source filtration (DSS) section 1 dim PD Brain Networks
(Chowdhury et al. 2018) Zigzag simplicial filtration (ZSF) section 1 dim zigzag PD Brain Networks
(Chung et al. 2015) Vietoris-Rips filtration (VR) section 0 dim Betti plots Brain networks
(Knyazeva et al. 2018) Vietoris-Rips filtration (VR) section 0-1 dim PD Brain networks
(Petri et al. 2014) Vietoris-Rips filtration (VR) section 1 dim PD Brain networks
(Yoo et al. 2016) Weighted simplex filtration (WS) section 0 dim persistence vineyards Brain Networks
(Huang and Ribeiro 2017) Weighted simplex filtration (WS) section 0-2 dim PD Collaboration networks
(Carstens and Horadam 2013) Vietoris-Rips filtration (VR) section 0-2 dim Betti numbers Collaboration networks
(Pal et al. 2017) Temporal filtration (TMP) 1 dim Betti numbers Collaboration networks
(Sizemore et al. 2016) Vietoris-Rips filtration (VR) section 0-3 dim Betti numbers PPI, brain and simulated weighted networks
(Schauf et al. 2016) Vietoris-Rips filtration (VR) section 0-2 dim PD Economy networks
(Gidea 2017) Vietoris-Rips filtration (VR) section 0-1 dim PD Finance networks
(Horak et al. 2009) CCL 0-11 dim PD Random, email and scale-free networks
(Dey et al. 2015) Functional metric graph filtration (FMG) section 0 dim PD Road networks
(Kim and Memoli 2018) ZSF 0 dim zigzag PD Dynamic biological networks
(Chowdhury and Mémoli 2018) Digraph filtration using persistent path homology (PPH) section 1 dim PD Cycle networks
(Hajij et al. 2018) Power filtration (POW) section 0-1 dim PD Dynamic communication networks
(Keil and Aktas 2018) Vertex function based filtration (VFB) section 0-1 dim PD Attributed social networks
(Gao and Li 2018) Power filtration (POW) section 0-1 dim PD Online social networks
(Carrière et al. 2019) Vertex function based filtration (VFB) section 0-1 dim PD Social, medical and biological networks
(Petri et al. 2013a; 2013b; Binchi et al. 2014) Vietoris-Rips filtration (VR) section 1 dim PB Social, infrastructural and biological networks