Vietoris-Rips Lifting (Graph to Complex)

[Jonas-Verhellen]

Although typically used for point cloud data, this method can be adapted to graphs by treating vertices as points and defining edges based on graph distances. A k-simplex is included if the pairwise distances between its vertices are all below a certain threshold.

To construct a Vietoris-Rips complex:

1. Define a distance metric based on the graph (e.g., shortest path distance).
2. Select a threshold distance.
3. Form simplices for all sets of vertices with pairwise distances less than the threshold distance.

We use nx.all_pairs_shortest_path_length to calculate the shortest path distances between all pairs of nodes in the graph. The VietorisRipsLifting class includes a distance_threshold parameter to specify the maximum allowed distance for simplex formation.

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[gbg141]

Hello @Jonas-Verhellen! Thank you for your submission. As we near the end of the challenge, I am collecting participant info for the purpose of selecting and announcing winners. Please email me (or have one member of your team email me) at guillermo_bernardez@ucsb.edu so I can share access to the voting form. In your email, please include:

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[gbg141]

Thanks!