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arXiv · 2408.11180

Any Graph is a Mapper Graph

Enrique G Alvarado·Robin Belton·Kang-Ju Lee·Sourabh Palande·Sarah Percival·Emilie Purvine·Sarah Tymochko
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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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Enrique G Alvarado, Robin Belton, Kang-Ju Lee, Sourabh Palande, Sarah Percival, Emilie Purvine, Sarah Tymochko. 2024-08-20. Any Graph is a Mapper Graph. https://arxiv.org/abs/2408.11180

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