Resolution limit

The resolution limit is a fundamental constraint on modularity-based community detection, identified by Fortunato and Barthelemy in 2007. It states that modularity-optimizing algorithms cannot detect communities whose total internal degree is smaller than the square root of the total degree of the network. In practice, this means that large networks hide their small communities: a perfectly valid community embedded in a local neighborhood may be merged into a larger community because the global modularity function cannot "see" it.

The resolution limit is not a bug in any particular algorithm. It is a property of the modularity quality function itself. It implies that community detection is inherently scale-dependent: different methods reveal structure at different resolutions. Multi-resolution approaches — such as the Potts model formulation of community detection — address this by introducing a resolution parameter that tunes the scale at which communities are detected.