Question: what is characteristic of adjacency matrix of all commutative diagram

want to write in maple code

to generate all commutative diagram 

with adjacency matrix

 

however, i only know a -> b, b-> c , a->d , d-> c

google no information about all commutative diagram, 

 

another problem is

would like to enrich theory , however, do not know how to connect property such as equations with diagram

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