  This study introduces a new districting approach using the US Postal Service
network to measure community connectivity. We combine Topological Data Analysis
with Markov Chain Monte Carlo methods to assess district boundaries' impact on
community integrity. Using Iowa as a case study, we generate and refine
districting plans using KMeans clustering and stochastic rebalancing. Our
method produces plans with fewer cut edges and more compact shapes than the
official Iowa plan under relaxed conditions. The low likelihood of finding
plans as disruptive as the official one suggests potential inefficiencies in
existing boundaries. Gaussian Mixture Model analysis reveals three distinct
distributions in the districting landscape. This framework offers a more
accurate reflection of community interactions for fairer political
representation.
