One can discuss the ordering and the equivalence of diagrams. From the
first, one might stipulate that one diagram is larger than another if
it has all the nodes of the smaller; likewise all the links. If
is one diagram and 
is another,
then 
would mean
In short, subdiagrams would be smaller. However we are also interested in comparing paths through diagrams, and not necessarily the diagrams themselves. So mappings between diagrams could hold our interest because of wanting to embed a given path in an equivalent diagram which could be more favorable.
There are many other reasons for such an interest in mappings. Drawings can be laid out quite differently as the groupings of nodes are changed or the crossing of links is avoided; regular expressions can be rearranged according to the distributive and associative laws, and so on. At the very least, mappings between different formulations are desirable, to be able to compare them to one another, and to recognize equivalent formulations.