Eccentricity Lifting (Graph to Simplicial) - geometric-intelligence/TopoBench GitHub Wiki

The EccentricityComplexLifting class provides a method to transform a graph into a simplicial complex based on the eccentricity of its vertices. This lifting captures the topology of the graph by forming simplices that reflect the hierarchical structure of vertex neighborhoods, determined by the eccentricity distance. This provides a measure of the spread of each vertex within the graph.

For each vertex, its neighborhood within the eccentricity distance is determined. Simplices are formed from combinations of vertices within each neighborhood. The node features from the original graph are preserved and added to the corresponding nodes in the simplicial complex. Potentially of interest for networks where the spread or influence of a node is of interest, such as in epidemic modeling or information propagation.

From https://github.com/pyt-team/challenge-icml-2024/pull/10