<p>Community detection has garnered extensive attention due to its capacity to unveil valuable insights hidden within networks. Nevertheless, the performance of existing methods significantly deteriorates when faced with unclear community structures. To address this issue, this paper proposes CSE_MOPSO, a novel algorithm integrating community structure enhancement with multi-objective particle swarm optimization. First, we employ fuzzy neighbourhoods and k-nearest neighbours to calculate local density, improving central node identification accuracy. Second, we design a link prediction index considering both direct and indirect node effects, using common and non-common neighbour information to enhance community structure. Third, a tailored multi-objective particle swarm optimization (MOPSO) strategy further optimizes preliminary communities, addressing fragmented sizes and ambiguous node attributions. Experimental results on six sets of Lancichinetti–Fortunato–Radicchi (LFR) benchmark networks (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$N=1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>K–10K, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mu \in [0.1, 0.8]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.8</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>) and eight real-world networks demonstrate that CSE_MOPSO achieves typical NMI improvements of 0.15–0.25 against the strongest baselines when <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mu \ge 0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>≥</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation>, with modularity <i>Q</i> gains up to 0.05 on real-world networks.</p>

Community detection based on community structure enhancement and multi-objective particle swarm optimization

期刊论文
发表日期：

2026年4月21日

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Yan Sun,
Fanyu Zhang,
Mingyuan Bi,
Junliang Shang,
Defu Qiu,
Hanxiang Wang,
Jin-Xing Liu

摘要

Community detection has garnered extensive attention due to its capacity to unveil valuable insights hidden within networks. Nevertheless, the performance of existing methods significantly deteriorates when faced with unclear community structures. To address this issue, this paper proposes CSE_MOPSO, a novel algorithm integrating community structure enhancement with multi-objective particle swarm optimization. First, we employ fuzzy neighbourhoods and k-nearest neighbours to calculate local density, improving central node identification accuracy. Second, we design a link prediction index considering both direct and indirect node effects, using common and non-common neighbour information to enhance community structure. Third, a tailored multi-objective particle swarm optimization (MOPSO) strategy further optimizes preliminary communities, addressing fragmented sizes and ambiguous node attributions. Experimental results on six sets of Lancichinetti–Fortunato–Radicchi (LFR) benchmark networks ( $N=1$ $N = 1$ K–10K, $\mu \in [0.1, 0.8]$ $μ \in [0.1, 0.8]$ ) and eight real-world networks demonstrate that CSE_MOPSO achieves typical NMI improvements of 0.15–0.25 against the strongest baselines when $\mu \ge 0.5$ $μ \geq 0.5$ , with modularity Q gains up to 0.05 on real-world networks.