Honors Theses


James Worth Bagley College of Engineering


James Worth Bagley College of Engineering


Department of Electrical and Computer Engineering


Department of Electrical and Computer Engineering


Bachelor of Science


Software Engineering

Document Type

Honors Thesis


This paper covers the potential applications of using the spectral analysis of a graph’s Laplacian matrix to gene co-expression networks. The general idea is to take publically available genetic data from cancer studies, organize them into gene co-expression networks, and analyze them using Spectral Graph theory. The publically available cancer study data includes files that show the occurrence of several different genes within a single person’s genetic data (given by fragments per kilobase million). The research takes the data of several patients and organizes them into a table. From there, each gene’s occurrence is measured against every other gene’s occurrence using Pearson correlation values, resulting in another table of pairs of genes and their correlation values. For each line, a gene, another gene, and their Pearson correlation value are represented in three columns corresponding to each aforementioned piece of data. Only genes that have a Pearson correlation value above a certain threshold were added to this file so that the file represents only significant correlations between genes. This file could be interpreted as an edge list for a gene co-expression network, which is a graph showing connections between genes. Each gene represents a single node of the graph, and every line of the file contained the connection between two genes, this connection being the edge between two nodes. With the file able to be interpreted as a graph, Spectral Graph theory concepts applied to it very naturally, allowing us to extract the second-smallest eigenvalue of the graph’s Laplacian matrix and the degree of zero eigenvalues, which gave us an understanding of the graph’s structure.

Publication Date


First Advisor

Perkins, Andy

Second Advisor

Nanduri, Bindu

Third Advisor

Oppenheimer, Seth