HARP Research

HARP’s work involved generalized graphs and hypergraphs with richer relationships than a conventional node-and-edge diagram. Vertices, edges, layers, direction, spin, and interactions all needed software representations before they could become a useful visual system.

My contribution went beyond drawing graphs. I worked on the Python structures and operations that let researchers create, manipulate, test, and then visualize those ideas in HarpGraph2. The challenge was to understand an unfamiliar mathematical domain well enough to turn its rules into dependable software behavior.

I developed an object-oriented Python API for Hurwitz quaternion integers with more than 15 core operations. The work included Euclidean division, conjugation, equivalence handling, and unit tests for both correct results and exception behavior.

Whole-integer and half-integer forms needed explicit representation. The supplied project material shows the constructor below as the public interface for creating both forms:

from hurwitz import HurwitzQuaternion

q1 = HurwitzQuaternion(1, 2, 3, 4)
# 1 + 2i + 3j + 4k

q_half = HurwitzQuaternion(
    1, 3, 5, 7, half=True
)

Why the tests mattered

In research software, a plausible-looking result is not enough. pytest coverage helped capture mathematical expectations as executable checks, including edge cases and invalid operations, so later graph work could rely on a stable abstraction.

The interface work used Python and Matplotlib to make complex graph data visible for research prototyping and validation. The completed GenGraph differentiates vertices, edges, layers, directional relationships, and spins so the output remains connected to the underlying model.

The work also included a Qiskit proof of concept exploring whether classical graph structures could be embedded into quantum circuits. That was an exploratory feasibility step within the broader research—not the central purpose of the project.