Whale optimization algorithm based on Markov chain is used for overlapping community discovery.

To address issues such as low search efficiency and reduced diversity in the later stages of the Whale Optimization Algorithm (WOA), this paper proposes a Markov Chain-based Whale Optimization Algorithm for overlapping community detection. To address the low search efficiency of traditional WOA caused by the lack of prior knowledge utilization, a Markov chain-based state decision mechanism is introduced. To tackle the low diversity in the late stages of WOA, a differential bidirectional crossover strategy is proposed. This strategy increases diversity by implementing bidirectional crossover on individuals entering the late search phase through screening. To address the low partitioning accuracy caused by redundant nodes during the initial overlapping community division, a topology-potential-based overlapping node optimization strategy is proposed. This strategy enhances the accuracy of overlapping communities by calculating and eliminating redundant nodes. Experiments on the LFR synthetic network and seven real-world networks demonstrate that MKWOA outperforms six mainstream comparison algorithms. On the LFR benchmark network, MKWOA achieves excellent or competitive normalized mutual information (NMI) values, particularly excelling when mixed parameters are high and community structures are ambiguous. MKWOA achieved the highest extended modularity (EQ) values on five of the seven real networks (including Karate, Polbooks, and Jazz). For instance, on the Polbooks network, its EQ value surpassed the second-best algorithm by approximately 9.5%. These results validate that the proposed strategy effectively enhances the algorithm's performance and robustness in overlapping community detection.