Date of Award

2023-12-01

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Advisor(s)

Amy E. Wagler

Abstract

Heuristic network statistics are used as a preliminary approach to identify change across networks. In networks where there is known node correspondence (KNC), conventional network comparison methods include taking a norm of the difference matrix, or calculating dissimilarity measures like DeltaCon and cut distance. Since different KNC measures provide varying insight to the network comparison problem, we propose employing Rank Score Characteristic Functions (RSCFs) and the rank-score process as a method for reaching a consensus when ranking quantified change across multiple pairs of networks â?? which is particularly useful for ranking change across subpopulations or subgraphs. Additionally, we propose a method to characterize the sampling distributions of three KNC measures using a nonparametric network. An innovative process for systematically simulating network data for given graph structures by means of distance correlation matrices, which are used within the nonparametric network bootstrap, will be detailed. These methods are motivated by two applications â?? one where there is a need to study change in survey response structures across time, and another where there is a need to identify differences in vole brain structures across two populations.

Language

en

Provenance

Recieved from ProQuest

File Size

184 p.

File Format

application/pdf

Rights Holder

Clarissa Reyes

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