[2205.05178] Magnitude and Topological Entropy of Digraphs
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Mathematics > Category Theory

arXiv:2205.05178 (math)
[Submitted on 10 May 2022 (v1), last revised 2 Aug 2023 (this version, v3)]

Title:Magnitude and Topological Entropy of Digraphs

Authors:Steve Huntsman
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Abstract:Magnitude and (co)weightings are quite general constructions in enriched categories, yet they have been developed almost exclusively in the context of Lawvere metric spaces. We construct a meaningful notion of magnitude for flow graphs based on the observation that topological entropy provides a suitable map into the max-plus semiring, and we outline its utility. Subsequently, we identify a separate point of contact between magnitude and topological entropy in digraphs that yields an analogue of volume entropy for geodesic flows. Finally, we sketch the utility of this construction for feature engineering in downstream applications with generic digraphs.
Comments: In Proceedings ACT 2022, arXiv:2307.15519
Subjects: Category Theory (math.CT); Discrete Mathematics (cs.DM); Combinatorics (math.CO)
Cite as: arXiv:2205.05178 [math.CT]
  (or arXiv:2205.05178v3 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2205.05178
Journal reference: EPTCS 380, 2023, pp. 254-267
Related DOI: https://doi.org/10.4204/EPTCS.380.15

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 10 May 2022 21:30:34 UTC (1,988 KB)
[v2] Sun, 10 Jul 2022 22:24:30 UTC (1,973 KB)
[v3] Wed, 2 Aug 2023 16:21:02 UTC (1,974 KB)
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