A Review of Community Detection Based on Modularity Optimization in Complex Networks

Abstract

Community detection is one of the most interesting issues nowadays, especially for complex networks. The main problem is to divide these networks into partitions called communities, which are characterized by dense connections inside each part but sparse connections between them. Most networks in the real world display a community structure that must be detected and recovered. There are many approaches (techniques) for detecting communities, which may be arranged in classes according to various bases, like the operational method or the adopted definition of community. However, just a few desired algorithms are applied and adopted for identifying communities, like optimization of quality functions. This review highlights the existing modularity-based community detection methods. These methods are computational approaches based on optimization since they maximize the objective function modularity for each possible partitioning. Also, more attention was paid to demonstrating the quality functions that measure the goodness of these partitions, including the modularity function and its various expressions for different types of networks, which currently appear to be the most promising. In this review, computations are made for partitioning and detecting communities of different networks using the convexified modularity maximization algorithm (CMM), and then these partitions are measured using various quality functions. In addition, a derivation of an augmenting Lagrange multiplier is introduced to optimize the solution, which is implemented by the alternating direction multipliers method (ADMM) algorithm. So, such performance will help researchers find the best methods and choose a suitable quality function relevant to future work.