  It is well-known that community detection methods based on modularity
optimization often fails to discover small communities. Several objective
functions used for community detection therefore involve a resolution parameter
that allows the detection of communities at different scales. We provide an
explicit upper bound on the community size of communities resulting from the
optimization of several of these functions. We also show with a simple example
that the use of the resolution parameter may artificially force the complete
disaggregation of large and densely connected communities.
