Q. about {0,1}-matrices.

[Jonathan Post]

I suggest a better name for "binary matrices which are not robust": gracile.

A126603 versus A125507.

Robust and Gracile are antonyms, used as relative terms in paleoanthroplogy,
generally of bone proportions (i.e., thickness relative to length).
Frequently used for Australopithecus, as in "Australopithecus afarensis and
Australopithecus are known as gracile australopithecines, because of their
relatively lighter build, especially in the skull and teeth. Paranthropus
aethiopicus, robustus, and boisei are robust australopithecines."
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