Object graphs should reflect the basic notion that mathematical objects or classes of objects (and by extension mathematical theories) are synthesized from sets and a set of properties and for which certain operations are defined which are often maps.
Also, in the case of object graphs, The drawing itself, or expression into a graph , is a structuring process that reflects the structure of the mathematical or algebraic theory.
this is akin , though in a less formal way, to object-oriented class diagrams. The main difference is that common operations and properties are listed separately from classes.
Of course the real major difference between theorem graphs and class diagrams is that both exist for different purposes: while the former ends up as a (hopefully interactive) visualization, the latter gets implemented as software.
Thus theorem graphs will not have to contain patterns for communication and maintenance of classes of objects.
Nonetheless a formal mapping from math object graphs to class diagrams could be highly desirable unless completely covered by the presence of such object libraries.
Example of a couple of group theoretic objects
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