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Conceptual Mathematics, Second Edition by Stephen H. Schanuel, F. William Lawvere

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SESSION 17

Some uses of graphs

1.  Paths

What sort of problem might suggest using the category of irreflexive graphs, image Remember that an object of this category looks like this:

image

Why is this kind of picture useful? The dots may stand for physical locations and the arrows may represent roads joining them, so that this picture is a schematic road map and may be useful to plan a trip. (In practice, a two-way road is really two one way roads, separated by a patch of grass or at least a line of paint.) Dots may represent states of a physical system, and ...

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