  Cyclic systems of dichotomous random variables have played a prominent role
in contextuality research, describing such experimental paradigms as the
Klyachko-Can-Binicoglu-Shumovky, Einstein-Podolsky-Rosen-Bell, and Leggett-Garg
ones in physics, as well as conjoint binary choices in human decision making.
Here, we understand contextuality within the framework of the
Contextuality-by-Default (CbD) theory, based on the notion of probabilistic
couplings satisfying certain constraints. CbD allows us to drop the commonly
made assumption that systems of random variables are consistently connected.
Consistently connected systems constitute a special case in which CbD
essentially reduces to the conventional understanding of contextuality. We
present a theoretical analysis of the degree of contextuality in cyclic systems
(if they are contextual) and the degree of noncontextuality in them (if they
are not). By contrast, all previously proposed measures of contextuality are
confined to consistently connected systems, and most of them cannot be extended
to measures of noncontextuality. Our measures of (non)contextuality are defined
by the L_{1}-distance between a point representing a cyclic system and the
surface of the polytope representing all possible noncontextual cyclic systems
with the same single-variable marginals. We completely characterize this
polytope, as well as the polytope of all possible probabilistic couplings for
cyclic systems with given single-variable marginals.[...]
