Graduation Year
2025
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Second Department
Computer Science
Reader 1
Sarah Cannon
Reader 2
Christina Edholm
Terms of Use & License Information
Rights Information
© 2025 Anne K Friedman
Abstract
This paper aims to better characterize dual graphs derived from state districting maps by developing random graph models that replicate their structural properties. Dual graphs provide a simplified way to represent districting maps, making it computationally feasible to analyze their structure. These representations enable researchers, legislators, and courts to assess district compactness, detect signs of gerrymandering, and generate alternative districting plans. A deeper understanding of the structural patterns of these dual graphs can help researchers choose or design more effective algorithms for redistricting analysis. The random graph models developed in this study serve as testbeds for evaluating algorithmic approaches to creating fair and unbiased districting plans. Through a variety of edge-adding and edge-removal strategies, this paper identifies models that closely approximate three key statistics of real-world dual graphs: the average degree, the spanning tree constant asymptote, and the average spanning tree constant.
Recommended Citation
Friedman, Anne, "Random Graph Models for Dual Graphs" (2025). Scripps Senior Theses. 2598.
https://scholarship.claremont.edu/scripps_theses/2598
Data Repository Link
https://github.com/afr13dman/senior-thesis
