Detecting communities in large networks has drawn much attention over the
years. While modularity remains one of the more popular methods of community
detection, the so-called resolution limit remains a significant drawback. To
overcome this issue, it was recently suggested that instead of comparing the
network to a random null model, as is done in modularity, it should be compared
to a constant factor. However, it is unclear what is meant exactly by
"resolution-limit-free", that is, not suffering from the resolution limit.
Furthermore, the question remains what other methods could be classified as
resolution-limit-free. In this paper we suggest a rigorous definition and
derive some basic properties of resolution-limit-free methods. More
importantly, we are able to prove exactly which class of community detection
methods are resolution-limit-free. Furthermore, we analyze which methods are
not resolution-limit-free, suggesting there is only a limited scope for
resolution-limit-free community detection methods. Finally, we provide such a
natural formulation, and show it performs superbly
