Magnitude homology and Euler characteristics of directed acyclic graphs

2026/07/25 by Steve Huntsman
#math.AT #math.CO

paper · pdf

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.

Citations

• Geometry-Aware Edge Pooling for Graph Neural Networks
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Related

• Eulerian magnitude homology: subgraph structure and random graphs
• Computing eulerian magnitude homology
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• Girth, magnitude homology and phase transition of diagonality