  This paper aims at comparing two coupling approaches as basic layers for
building clustering criteria, suited for modularizing and clustering very large
networks. We briefly use "optimal transport theory" as a starting point, and a
way as well, to derive two canonical couplings: "statistical independence" and
"logical indetermination". A symmetric list of properties is provided and
notably the so called "Monge's properties", applied to contingency matrices,
and justifying the $\otimes$ versus $\oplus$ notation. A study is proposed,
highlighting "logical indetermination", because it is, by far, lesser known.
Eventually we estimate the average difference between both couplings as the key
explanation of their usually close results in network clustering.
