Abstract

Network science continues to be an area of growing interest. In this thesis we introduce new methods of analyzing the structure of networks through the use of persistent homology. We propose the notion of a network's persistent surface, which allows us to visualize a vertex's relation to the whole network from a purely homological point of view. We further introduce a method of persistent surface community detection that finds vertices that play the same structural role in the network. We describe how these concepts provide the basis for an equivalence class among the vertices of a network, and provide many examples of ways in which these ideas are useful in both real and theoretical networks. We also connect persistent surface community using our Persistent Surface Algorithm (PSA) to other well-established concepts in network science. We expect that persistent homology tools will become increasingly important in network science as current methods hit their limitations.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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