Topological and Geometric Reconstruction of Metric Graphs in $\mathbb{R}^n$

TL;DR

This paper introduces an algorithm for reconstructing the topology of an embedded metric graph in Euclidean space from a well-sampled finite subset, advancing the understanding of geometric graph reconstruction.

Contribution

The paper presents a novel algorithm that accurately estimates the topology of embedded metric graphs from finite samples, improving existing methods.

Findings

Successfully reconstructs graph topology from samples

Performs well with well-sampled data sets

Advances geometric graph reconstruction techniques

Abstract

We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.