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<p>This paper investigates the spectral radius of <i>k</i>-uniform directed hypergraphs. We derive sharp bounds of the spectral radius based on both dual and multiple outdegree parameters, comparing different estimation techniques to highlight their respective advantages. The necessary and sufficient conditions for achieving tight bounds are obtained by conceptualizing outdegree regularity or outdegree semiregularity. Further, novel bounds of spectral radius are established by virtue of the average 2-outdegree via similarity transformation. Numerical examples are provided to illustrate the effectiveness and applicability of the theoretical results.</p>

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Sharp Bounds and Structural Insights: Spectral Radius for Directed Hypergraphs

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Gang Wang,
  • Quanfeng Xin,
  • Hongchun Sun

摘要

This paper investigates the spectral radius of k-uniform directed hypergraphs. We derive sharp bounds of the spectral radius based on both dual and multiple outdegree parameters, comparing different estimation techniques to highlight their respective advantages. The necessary and sufficient conditions for achieving tight bounds are obtained by conceptualizing outdegree regularity or outdegree semiregularity. Further, novel bounds of spectral radius are established by virtue of the average 2-outdegree via similarity transformation. Numerical examples are provided to illustrate the effectiveness and applicability of the theoretical results.