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Representation of graphs by means of generalized metrics. (English) Zbl 1470.62076

Summary: The paper deals with spaces with metrics of nonnegative integer values, called here discrete gem spaces. We recall the concept of proper continuity for such spaces. Undirected connected graphs can be seen as such spaces and we show that they form the class of spaces satisfying the property corresponding to convexity in Euclidean spaces. Moreover, the whole category of discrete gem spaces and properly continuous maps is shown to be equivalent to a subcategory of the category of connected looped digraphs and their homomorphisms.

MSC:

62H22 Probabilistic graphical models
62R20 Statistics on metric spaces
54E70 Probabilistic metric spaces
05C90 Applications of graph theory
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