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<p>Per an earlier work, nodes with lower local clustering coefficient (LCC), but larger degree centrality (DEG), are more likely to incur a larger BWC (betweenness centrality); in this research, we hypothesize that such nodes could be potentially classified as the core nodes of the network as well. We propose to conduct PCA (principal component analysis) of a dataset comprising of the LCC′ (=1&#xa0;−&#xa0;LCC) and DEG values of the nodes in a complex network and claim that the weighted average principal component (WAPC) score could be used as the <i>coreness index</i> of a node: a quantitative measure of the extent to which a node plays the role of a core node in the network. We propose that nodes with positive and negative WAPC scores could be, respectively, categorized as core nodes and peripheral nodes. We measure the fractions of edges between any two core nodes (<i>f</i><sub>cc</sub>), between any two peripheral nodes (<i>f</i><sub>pp</sub>) and between a core node and a peripheral node (<i>f</i><sub>cp</sub>). We propose to categorize a real-world network as core–core-heavy if <i>f</i><sub>cc</sub>&#xa0;−&#xa0;<i>f</i><sub>cp</sub> &gt; 0.02, core–peripheral-heavy if <i>f</i><sub>cp</sub>&#xa0;−&#xa0;<i>f</i><sub>cc</sub> &gt; 0.02 and core–core–peripheral balanced if |<i>f</i><sub>cc</sub>&#xa0;−&#xa0;<i>f</i><sub>cp</sub>| ≤ 0.02.</p>

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Node-betweenness-based principal component model for core–periphery structural analysis of complex networks

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Natarajan Meghanathan

摘要

Per an earlier work, nodes with lower local clustering coefficient (LCC), but larger degree centrality (DEG), are more likely to incur a larger BWC (betweenness centrality); in this research, we hypothesize that such nodes could be potentially classified as the core nodes of the network as well. We propose to conduct PCA (principal component analysis) of a dataset comprising of the LCC′ (=1 − LCC) and DEG values of the nodes in a complex network and claim that the weighted average principal component (WAPC) score could be used as the coreness index of a node: a quantitative measure of the extent to which a node plays the role of a core node in the network. We propose that nodes with positive and negative WAPC scores could be, respectively, categorized as core nodes and peripheral nodes. We measure the fractions of edges between any two core nodes (fcc), between any two peripheral nodes (fpp) and between a core node and a peripheral node (fcp). We propose to categorize a real-world network as core–core-heavy if fcc − fcp > 0.02, core–peripheral-heavy if fcp − fcc > 0.02 and core–core–peripheral balanced if |fcc − fcp| ≤ 0.02.