2022/10/18 by Levent Batakci, Abigail Branson, Batakci, Levent +9
Computer Science · #Computational Geometry (cs.CG) #Data Management and Algorithms #Data Visualization and Analytics #FOS: Computer and information sciences #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2210.10181
openalex publication_date 2022/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such graphs, can we rank how similar they are, in such a way that we capture their geometric "shape" in the plane? In this paper we explore a method to compare two such embedded graphs, via a simplified combinatorial representation called a tail-less merge tree which encodes the structure based on a fixed direction. First, we examine the properties of a distance designed to compare merge trees called the branching distance, and show that the distance as defined in previous work fails to satisfy some of the requirements of a metric. We incorporate this into a new distance function called average branching distance to compare graphs by looking at the branching distance for merge trees defined over many directions. Despite the theoretical issues, we show that the definition is still quite useful in practice by using our open-source code to cluster data sets of embedded graphs.