Persistence homology of networks: methods and applications

Applied Network Science

Table 1 The comparison of filtrations

	Undirected network	Directed network	Weighted network	Unweighted network	Metric network	Dynamic network	Simplicial Complex	Ordered-tuple complex	Stable
Vietoris-Rips filtration (VR) section	✓		✓				✓		✓
Dowker sink and source filtration (DSS) section		✓	✓				✓		✓
Clique complex filtration (CCL) section	✓			✓			✓
Vertex-based clique filtration (VBCL) section	✓		✓				✓
k-clique filtration (kCL) section	✓		✓				✓
Weighted simplex filtration (WS) section	✓		✓				✓
Vertex function based filtration (VFB) section	✓		✓				✓		✓
Intrinsic Čech filtration (IC) section	✓			✓	✓		✓
Functional metric graph filtration (FMG) section	✓		✓		✓		✓		✓
Power filtration (POW) section	✓			✓			✓
Temporal filtration (TMP) section		✓		✓		✓	✓
Zigzag simplicial filtration (ZSF) section	✓			✓		✓	✓		✓
Digraph filtration using persistent path homology (PPH) section		✓	✓				✓		✓
Vietoris-Rips filtration under sym _a section	✓		✓				✓		✓
Directed Vietoris-Rips filtration section		✓	✓					✓	✓
Associated filtration of directed graphs section		✓	✓				✓		✓
Preorder filtration section		✓	✓					✓	✓