Title: A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs,
Abstract: Metric graphs are special types of metric spaces used to model and represent
simple, ubiquitous, geometric relations in data such as biological networks,
social networks, and road networks. We are interested in giving a qualitative
description of metric graphs using topological summaries. In particular, we
provide a complete characterization of the 1-dimensional intrinsic Cech
persistence diagrams for metric graphs using persistent homology. Together with
complementary results by Adamaszek et. al, which imply results on intrinsic
Cech persistence diagrams in all dimensions for a single cycle, our results
constitute important steps toward characterizing intrinsic Cech persistence
diagrams for arbitrary metric graphs across all dimensions.