Curvature Filtrations for Graph Generative Model Evaluation

Southern, Joshua; Wayland, Jeremy; Bronstein, Michael M.; Rieck, Bastian

doi:10.48550/arxiv.2301.12906

Cited by 2 publications

(1 citation statement)

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“…This was carried out, e.g., in [23], where a connection between Laplacian, persistence, and network circuit graphs was drawn. Another paper [24] addressed persistence, using the notion of discrete curvature for the evaluation of graph generative models. The clique complex is also a very natural way of transforming a graph into a possibly multidimensional complex.…”

Section: Persistent Homology For (Di)graphsmentioning

confidence: 99%

Exploring Graph and Digraph Persistence

Bergomi,

Ferri

2023

Algorithms

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Among the various generalizations of persistent topology, that based on rank functions and leading to indexing-aware functions appears to be particularly suited to catching graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies “simple” and “single-vertex” features in directed and undirected graphs, through which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the “sink” feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.

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Section: Persistent Homology For (Di)graphsmentioning

confidence: 99%

Exploring Graph and Digraph Persistence

Bergomi,

Ferri

2023

Algorithms

View full text Add to dashboard Cite

show abstract

Exploring Graph and Digraph Persistence

Bergomi,

Ferri

2023

Preprint

View full text Add to dashboard Cite

Among the various generalizations of persistent topology, the one based on rank functions and leading to indexing-aware functions appears to be particularly suited to catch graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies "simple" and "single-vertex" features in directed and undirected graphs, by which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the "sink" feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.

show abstract

Curvature Filtrations for Graph Generative Model Evaluation

Cited by 2 publications

References 0 publications

Exploring Graph and Digraph Persistence

Exploring Graph and Digraph Persistence

Exploring Graph and Digraph Persistence

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