Analysis of Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence

Conference paper
Part of the Abel Symposia book series (ABEL, volume 15)


We overview recent work on obtaining persistent homology based summaries of time-dependent data. Given a finite dynamic graph (DG), one first constructs a zigzag persistence module arising from linearizing the dynamic transitive graph naturally induced from the input DG. Based on standard results, it is possible to then obtain a persistence diagram or barcode from this zigzag persistence module. It turns out that these barcodes are stable under perturbations of the input DG under a certain suitable distance between DGs. We also overview how these results are also applicable in the setting of dynamic metric spaces, and describe a computational application to the analysis of flocking behavior.



We acknowledge funding from these sources: NSF-RI-1422400, NSF AF 1526513, NSF DMS 1723003, NSF CCF 1740761.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Department of Computer Science and EngineeringThe Ohio State UniversityColumbusUSA
  3. 3.Department of Computer Science and EngineeringUniversity of MinnesotaMinneapolisUSA

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