Fuzzy community detection in social networks using a genetic algortihm

Community structure in a network usually is an indicator of some important hidden pattern, and thus can deepen our understandings of some phenomenon and also enable useful applications. Even though the introduction of Newman's modularity stimulates a magnitude of modularity-based community detection methods, only a few of them are designed for uncovering fuzzy overlapping communities in a network, which in practice are really common in social networks. Considering that modularity maximization is NP-hard and that a genetic algorithm's ability to find fairly good solutions of an NP-hard problem, an O (n
²
) genetic algorithm for fuzzy community detection (GAFCD) is proposed based on the generalized modularity, a one-step extension of Newman's modularity. Crossover in GAFCD works as an outer-layer search framework that statistically determines sub search spaces with which a novel mutation operator finds the best partition in each sub search space. We compare our proposed GAFCD method with an existing fuzzy community detection algorithm, MULTICUT spectral FCM (MSFCM), and GALS, one of the most effective disjoint (or crisp) community detection, on 10 real world data sets; it is observed that GAFCD outperforms the other algorithms in terms of finding max-modularity communities. Furthermore, GAFCD is able to find both fuzzy partitions and crisp partitions while MSFCM can only find fuzzy partitions and GALS can only find crisp partitions. This unique feature makes GAFCD the first genetic algorithm for finding truly fuzzy (i.e., inclusive of both fuzzy and crisp communities) max-modularity community structure in a network.