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

Jun Li1,2, Yang Zhou3, Dingkun Guan4

  • 1Lanzhou Modern Vocational College, Lanzhou, 730300, China. lijun_lanzhou@163.com.

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|April 17, 2026
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Summary
This summary is machine-generated.

This study introduces a novel Markov Chain-based Whale Optimization Algorithm (MKWOA) to improve overlapping community detection. MKWOA enhances search efficiency and diversity, outperforming existing methods on benchmark and real-world networks.

Keywords:
Complex networksMarkov chainOverlapping communitySwarm intelligenceWhale optimization

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Area of Science:

  • Complex Networks
  • Computational Intelligence
  • Data Mining

Background:

  • Traditional Whale Optimization Algorithm (WOA) suffers from low search efficiency and reduced diversity in later stages.
  • Overlapping community detection is crucial for understanding complex network structures.
  • Existing methods often struggle with redundant nodes, impacting partitioning accuracy.

Purpose of the Study:

  • To propose a Markov Chain-based Whale Optimization Algorithm (MKWOA) for enhanced overlapping community detection.
  • To improve the search efficiency and diversity of the WOA.
  • To increase the accuracy of overlapping community partitioning.

Main Methods:

  • Incorporation of a Markov chain-based state decision mechanism to utilize prior knowledge.
  • Implementation of a differential bidirectional crossover strategy to enhance late-stage diversity.
  • Application of a topology-potential-based overlapping node optimization strategy to eliminate redundant nodes.

Main Results:

  • MKWOA demonstrated superior performance compared to six mainstream algorithms on LFR synthetic and seven real-world networks.
  • Achieved competitive Normalized Mutual Information (NMI) values on the LFR benchmark, especially under high mixed parameters and ambiguous structures.
  • Obtained the highest Extended Modularity (EQ) values on five real-world networks, significantly outperforming others on datasets like Polbooks.

Conclusions:

  • The proposed MKWOA effectively enhances performance and robustness in overlapping community detection.
  • The integration of Markov chains, differential crossover, and node optimization strategies addresses key limitations of traditional WOA.
  • MKWOA shows significant potential for analyzing complex network structures with overlapping communities.