  Community structure represents the local organization of complex networks and
the single most important feature to extract functional relationships between
nodes. In the last years, the problem of community detection has been
reformulated in terms of the optimization of a function, the Newman-Girvan
modularity, that is supposed to express the quality of the partitions of a
network into communities. Starting from a recent critical survey on modularity
optimization, pointing out the existence of a resolution limit that poses
severe limits to its applicability, we discuss the general issue of the use of
quality functions in community detection. Our main conclusion is that quality
functions are useful to compare partitions with the same number of modules,
whereas the comparison of partitions with different numbers of modules is not
straightforward and may lead to ambiguities.
