Honors Theses

Document Type

Thesis

Date of Completion

Spring 4-30-2026

Academic Year

2025-2026

Department

Math

Academic Major

Mathematics

Faculty Advisor

Jason Holland, Ph.D.

Abstract

Graphs are simple, visual representations of entities as nodes connected by edges. They are used to convey relationships within a system. Networks are comprised of interrelated entities that are not easily separable, producing complex, structured data. These can be seen in social groups, highway systems, and even in biological systems. This paper surveys concepts in graph theory for application to the analysis of network data to understand disease. The features of graphs provide a useful framework for thinking about relationships between different genes or proteins. The structure of graphs is also compatible with a variety of machine learning tools. Especially in large networks, which are commonly seen in biological systems, these tools are helpful in extracting information and providing insight into the functions of the system as a whole. Considering the increasingly quantitative nature of molecular biology research, this analysis will explore the potential for using graphs and network analysis to explore the pathophysiology of diseases. Polycystic ovarian syndrome (PCOS) was chosen for its multisystemic involvement, wide availability of data, and opportunity for future study. As a condition primarily characterized by a collection of symptoms rather than a clear mechanism, network analysis techniques can be used to convert sample data into quantitative metrics, analyze connections within the network, and propose possible patterns to study to create a stronger understanding of how PCOS works. This paper only aims to convey observed features and changes of the network between the PCOS and control conditions. Further study and experimental confirmation are needed to explain the results of this analysis.

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