  An important step in unveiling the relation between network structure and
dynamics defined on networks is to detect communities, and numerous methods
have been developed separately to identify community structure in different
classes of networks, such as unipartite networks, bipartite networks, and
directed networks. We show that both unipartite and directed networks can be
represented as bipartite networks, and their modularity is completely
consistent with that for bipartite networks, the detection of modular structure
on which can be reformulated as modularity maximization. To optimize the
bipartite modularity, we develop a modified adaptive genetic algorithm (MAGA),
which is shown to be especially efficient for community structure detection.
The high efficiency of the MAGA is based on the following three improvements we
make. First, we introduce a different measure for the informativeness of a
locus instead of the standard deviation, which can exactly determine which loci
mutate. This measure is the bias between the distribution of a locus over the
current population and the uniform distribution of the locus, i.e., the
Kullback-Leibler divergence between them. Second, we develop a reassignment
technique for differentiating the informative state a locus has attained from
the random state in the initial phase. Third, we present a modified mutation
rule which by incorporating related operation can guarantee the convergence of
the MAGA to the global optimum and can speed up the convergence process.
Experimental results show that the MAGA outperforms existing methods in terms
of modularity for both bipartite and unipartite networks.
