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.

翻译：数量与（余）赋权是丰富范畴中相当一般的构造，但迄今几乎仅在Lawvere度量空间背景下得到发展。基于拓扑熵能提供进入最大-加半环的合适映射这一观察，我们为流图构建了有意义的数量概念，并概述了其效用。随后，我们在有向图中找到数量与拓扑熵之间的另一个接触点，这产生了测地流体积熵的类似物。最后，我们勾勒了该构造在一般有向图的下游应用中用于特征工程的实用价值。