Reinventing the Triangles: Rule of Thumb for Assessing Detectability
This provides a practical tool for network analysts to determine detectability without needing full eigenspectrum information, though it is incremental as it builds on existing phase transition theories.
The paper tackles the problem of assessing whether a network has detectable community structure by developing a criterion based on the global clustering coefficient, which is simpler and faster than bootstrapping methods.
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.