Date of Award

8-9-2014

Document Type

Open Access Thesis

Department

Chemistry and Biochemistry

First Advisor

Joseph E. Johnson

Abstract

Networks are a vital part of nature and society, yet many aspects of how networks function are still largely unknown. From understanding the internet to biology, chemistry, and physics, networks play a role, but even some of the most basic questions about networks can be difficult to answer. How are two networks alike or different? How do networks within networks form and how can clusters be detected? As networks change with time, how can we monitor those changes? The answers to these questions are vitally important to humans’ understanding of the world. Better understanding of networks allows for things like more efficient electrical distribution grids and more reliable real-time network intrusion detection systems. It also allows for a better understanding of how nature forms networks like the bonds that form molecules and the networks that carry water from the mountains to the sea and back again. Network analysis and cluster detection is a dynamic area of mathematics featuring many different approaches. This research is intended to approach network analysis using Markov matrices and methods normally reserved for physical systems. Three methods were used in this project to illuminate network classification and behaviors: multi-order Renyi entropy comparisons, eigenvalues/eigenvectors analysis to detect network clusters, and property tables used to create networks with clusters. All three methods produced promising results and hint that this new way of viewing networks can reveal some information that previously lay hidden.

Rights

© 2014, John William Campbell

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