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The extension of curvature, which is historically defined in continuous spaces, to discrete objects such as graphs presents new opportunities and challenges for application. In this work, we review recent notions of graph curvature parameterized by different distances on a graph. We explore the relationship between node-level curvature and well-established node-centrality measures on synthetic and real-world graphs in order to better understand their relationship and what novel information the curvature can reveal about a network. We end with a discussion of outstanding questions and applications.

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An Exploration of Graph Distances, Graph Curvature, and Applications to Network Analysis

  • 章节

  • 发表日期：

    2025年

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  • Kasia Jankiewicz,
  • Manasa Kesapragada,
  • Anna Konstorum,
  • Kathryn Leonard,
  • Nazia Riasat,
  • Michelle Snider

摘要

The extension of curvature, which is historically defined in continuous spaces, to discrete objects such as graphs presents new opportunities and challenges for application. In this work, we review recent notions of graph curvature parameterized by different distances on a graph. We explore the relationship between node-level curvature and well-established node-centrality measures on synthetic and real-world graphs in order to better understand their relationship and what novel information the curvature can reveal about a network. We end with a discussion of outstanding questions and applications.