In this paper, we first discuss the definition of modularity (Q) used as a
metric for community quality and then we review the modularity maximization
approaches which were used for community detection in the last decade. Then, we
discuss two opposite yet coexisting problems of modularity optimization: in
some cases, it tends to favor small communities over large ones while in
others, large communities over small ones (so called the resolution limit
problem). Next, we overview several community quality metrics proposed to solve
the resolution limit problem and discuss Modularity Density (Qds) which
simultaneously avoids the two problems of modularity. Finally, we introduce two
novel fine-tuned community detection algorithms that iteratively attempt to
improve the community quality measurements by splitting and merging the given
network community structure. The first of them, referred to as Fine-tuned Q, is
based on modularity (Q) while the second one is based on Modularity Density
(Qds) and denoted as Fine-tuned Qds. Then, we compare the greedy algorithm of
modularity maximization (denoted as Greedy Q), Fine-tuned Q, and Fine-tuned Qds
on four real networks, and also on the classical clique network and the LFR
benchmark networks, each of which is instantiated by a wide range of
parameters. The results indicate that Fine-tuned Qds is the most effective
among the three algorithms discussed. Moreover, we show that Fine-tuned Qds can
be applied to the communities detected by other algorithms to significantly
improve their results