# Categorified Reeb Graphs

@article{Silva2016CategorifiedRG, title={Categorified Reeb Graphs}, author={Vin de Silva and E. Munch and Amit K. Patel}, journal={Discrete \& Computational Geometry}, year={2016}, volume={55}, pages={854-906} }

The Reeb graph is a construction which originated in Morse theory to study a real-valued function defined on a topological space. More recently, it has been used in various applications to study noisy data which creates a desire to define a measure of similarity between these structures. Here, we exploit the fact that the category of Reeb graphs is equivalent to the category of a particular class of cosheaf. Using this equivalency, we can define an ‘interleaving’ distance between Reeb graphs…

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## 106 Citations

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