一种使用大小同调的中心性度量
A Centrality Measure Using Magnitude Homology
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中文总结 AI 辅助
基于大小同调的进展，开发衡量图中节点中心性的新局部度量，该度量受相对同调启发，考虑去顶点时大小同调变化，满足相关属性，带来中心性研究新视角。
中文摘要 AI 辅助
度量空间的大小构成一种富有表现力的不变量，它包含许多不同的几何拓扑不变量。基于大小同调（一种恢复大小的双分次同调理论）的最新进展，我们开发了一种新颖的局部度量来衡量图中节点的中心性或重要性。我们的度量受相对同调概念的启发，因为它考虑去除一个顶点时大小同调的变化。我们表明，我们提出的度量满足中心性度量合理预期应具备的几个属性，并通过与几种既定的中心性度量进行比较，证明我们引入了一种关于中心性的新视角。
英文摘要
The magnitude of a metric space constitutes an expressive invariant that subsumes numerous different geometrical-topological invariants. Building on recent advances in magnitude homology, i.e., a bigraded homology theory that recovers the magnitude, we develop a novel local measure of the centrality or importance of nodes in a graph. Our measure is inspired by the concept of relative homology as it considers the change in magnitude homology when removing a vertex. We show that our proposed measure satisfies several properties a centrality measure is reasonably expected to respect and demonstrate that we introduce a new perspective on centrality by comparing to several established centrality measures.
