  Statistical significance of network clustering has been an unresolved problem
since it was observed that community detection algorithms produce false
positives even in random graphs. After a phase transition between undetectable
and detectable cluster structures was discovered, the connection between
spectra of adjacency matrices and detectability limits were shown, and both
were calculated for a wide range of networks with arbitrary degree
distributions and community structure. In practice the full eigenspectrum is
not known, and whether a given network has any communities within detectability
regime cannot be easily established. Based on the global clustering coefficient
we construct a criterion telling whether in an undirected, unweighted network
there is some/no detectable community structure, or if the network is in a
transient regime. The method is simple and faster than methods involving
bootstrapping.
