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arXiv · 2607.23357

Magnitude homology and Euler characteristics of directed acyclic graphs

Steve Huntsman
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Abstract

We develop a scalable approach to computing the magnitude homology Euler characteristic for directed acyclic graphs based on decategorification. Along with motivating mathematical results and some simple controlled examples, we deploy the Euler characteristic in a proof of concept application to the dynamic analysis of multilayer perceptrons, recovering class-discriminative structure while holding simpler subgraph properties fixed.

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Steve Huntsman. 2026-07-25. Magnitude homology and Euler characteristics of directed acyclic graphs. https://arxiv.org/abs/2607.23357

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