Date of Thesis

Spring 2025

Description

We introduce linear invariants of hypergraphs as a way to study hypergraphs by their tensor representations. Our primary research goal is to determine what information linear invariants capture about the hypergraphs they arise from. We first investigate the centroid, which is shown to determine the connected components of a hypergraph. Next, we study the derivations of a hypergraph, and use this linear invariant to define a quotient operator $Q_\mathrm{Der}$ on the collection of all hypergraphs. This operator is shown to be a closure operator in that $Q_\mathrm{Der}(Q_\mathrm{Der}(\mathcal{H}))=Q_\mathrm{Der}(\mathcal{H})$ for any hypergraph $\mathcal{H}$. We apply the operator $Q_\mathrm{Der}$ to synthetically generated hypergraphs, exploring what features of a hypergraph it detects, and we discuss how this operator could be applied to hypergraphs arising from real data.

Keywords

hypergraphs, derivations, linear invariants, tensors, centroid, quotient graphs, quotient hypergraphs

Access Type

Honors Thesis

Degree Type

Bachelor of Science

Major

Mathematics

Second Major

Computer Science

First Advisor

Peter Brooksbank

Second Advisor

Lucas Waddell

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