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Any Graph is a Mapper Graph

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arxiv 2408.11180 v1 pith:BHLNN2CI submitted 2024-08-20 math.AT cs.CG

Enrique G Alvarado , Robin Belton , Kang-Ju Lee , Sourabh Palande , Sarah Percival , Emilie Purvine , Sarah Tymochko This is my paper · ORCID
classification math.ATcs.CG
keywords mappergraphalgorithmdataparametersaffirmativelyanalysisanswer
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abstract

The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper parameters such that the output Mapper graph of $X$ is isomorphic to $G$? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Stable and Theoretically Grounded Gromov-Wasserstein Distance for Reeb Graph Comparison using Persistence Images

    cs.CG 2025-07 reject novelty 6.0 of 10

    The authors introduce RGWp, a Gromov-Wasserstein distance for Reeb graphs with a symmetric Reeb radius and persistence-image weighting, and present a stability proof that contains unproven structural assumptions.

  2. $k$-means considered harmful: On arbitrary topological changes in Mapper complexes

    cs.CG 2025-07 conditional novelty 4.0 of 10

    Fixed-count clustering, such as k-means, can force Mapper complexes to display arbitrary, misleading topological features.

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