  Recent research has shown that virtually all algorithms aimed at the
identification of communities in networks are affected by the same main
limitation: the impossibility to detect communities, even when these are
well-defined, if the average value of the difference between internal and
external node degrees does not exceed a strictly positive value, in literature
known as detectability threshold. Here, we counterintuitively show that the
value of this threshold is inversely proportional to the intrinsic quality of
communities: the detection of well-defined modules is thus more difficult than
the identification of ill-defined communities.
