  Borgs et al. [2016] investigated essential requirements for communities in
preference networks. They defined six axioms on community functions, i.e.,
community detection rules. Though having elegant properties, the practicality
of this axiom system is compromised by the intractability of checking two
critical axioms, so no nontrivial consistent community function was reported
inBorgs et al. [2016] By adapting the two axioms in a natural way, we propose
two new axioms that are efficiently-checkable. We show that most of the
desirable properties of the original axiom system are preserved. More
importantly, the new axioms provide a general approach to constructing
consistent community functions. We further find a natural consistent community
function that is also enumerable and samplable, answering an open problem in
the literature.
