Persistent Homology: From Networks to Topological Features

1. Egocentric Network → Filtration Process

Click to add nodes and watch how the simplicial complex grows as we increase the filtration radius.

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Connected Components (H₀): 0 | Loops (H₁): 0

2. Persistence Barcode Diagram

Visual representation of topological features' birth and death during filtration.

H₀ Persistence (Components)

H₁ Persistence (Loops)

3. Persistence Diagram

Each point represents a topological feature. Distance from diagonal indicates persistence.