Magnitude and Topological Entropy of Digraphs

Magnitude and (co)weightings are quite general constructions in enriched categories, yet they have been developed almost exclusively the context of Lawvere metric spaces. We construct a meaningful notion magnitude for flow graphs based on observation that topological entropy provides suitable map into max-plus semiring, we outline its utility. Subsequently, identify separate point contact between digraphs yields an analogue volume geodesic flows. Finally, sketch utility this construction feature engineering downstream applications with generic digraphs.