  We have analyzed the detectability limits of network communities in the
framework of the popular Girvan and Newman benchmark. By carefully taking into
account the inevitable stochastic fluctuations that affect the construction of
each and every instance of the benchmark, we come to the conclusions that the
native, putative partition of the network is completely lost even before the
in-degree/out-degree ratio becomes equal to the one of a structure-less
Erd\"os-R\'enyi network. We develop a simple iterative scheme, analytically
well described by an infinite branching-process, to provide an estimate of the
true detectability limit. Using various algorithms based on modularity
optimization, we show that all of them behave (semi-quantitatively) in the same
way, with the same functional form of the detectability threshold as a function
of the network parameters. Because the same behavior has also been found by
further modularity-optimization methods and for methods based on different
heuristics implementations, we conclude that indeed a correct definition of the
detectability limit must take into account the stochastic fluctuations of the
network construction.
