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This paper aims at comparing two coupling approaches as basic layers forbuilding clustering criteria, suited for modularizing and clustering very largenetworks. We briefly use "optimal transport theory" as a starting point, and away as well, to derive two canonical couplings: "statistical independence" and"logical indetermination". A symmetric list of properties is provided andnotably 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 keyexplanation of their usually close results in network clustering.

Independence versus Indetermination: basis of two canonical clustering criteria