# Claremont Topology Seminar: Elena Wang (Michigan State University)

## April 30 @ 3:00 pm - 4:00 pm

We welcome all undergraduates and graduate students to attend topology seminar!

Speaker: Elena Wang (Michigan State University)

Title: A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance

Abstract: Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between graphs and present a metric to measure the distance between two geometric graphs via merge trees. In order to preserve as much useful information as possible from the original data, we introduce a way of rotating the sublevel set to obtain the merge trees via the idea of the directional transform. We represent the merge trees using a surjective multi-labeling scheme, and then compute the distance between two representative matrices. Our distance not only has theoretically desirable qualities but can also be approximated in polynomial time. We illustrate its utility by implementation on a *Passiflora* leaf data set.