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<p>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 <i>X</i> and a graph <i>G</i>, does there exist a choice of Mapper parameters such that the output Mapper graph of <i>X</i> is isomorphic to <i>G</i>? We provide explicit constructions that affirmatively answer this question. Our results demonstrate that it is possible to select Mapper parameters to generate a given graph, illustrating the flexibility of the Mapper algorithm.</p>

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Any Graph is a Mapper Graph

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Enrique G Alvarado,
  • Robin Belton,
  • Kang-Ju Lee,
  • Sourabh Palande,
  • Sarah Percival,
  • Emilie Purvine,
  • Sarah Tymochko

摘要

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 choice of Mapper parameters such that the output Mapper graph of X is isomorphic to G? We provide explicit constructions that affirmatively answer this question. Our results demonstrate that it is possible to select Mapper parameters to generate a given graph, illustrating the flexibility of the Mapper algorithm.