发表机构
University of Liverpool（利物浦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对Katz中心性的Top-k场景提出公平图设计问题，开发了可扩展算法BLADE，用更少编辑实现目标群体比例的Top-k公平排名，且可扩展到大型真实图。
AI 中文摘要
中心性度量被广泛用于对网络数据中的节点进行排序，但针对图中心性的公平干预通常针对全局分数质量或修改中心性算子，而非控制显示的Top-k排名中出现的节点。我们针对Katz中心性研究这一Top-k场景：给定目标群体比例、可允许的有向边添加集合和公平容忍度，目标是找到最小的编辑集合，使得其生成的Katz Top-k排名满足目标表示约束。我们将该问题形式化为公平Top-k Katz中心性设计问题，并证明最小编辑目标是强不可近似的，除非P=NP，否则排除了最坏情况多项式时间近似保证。随后我们推导了闭式Katz灵敏度表达式，表明有用的编辑是边界驱动的：它们必须帮助Top-k集合之外的可提升节点超过集合内的对立节点。基于该结构，我们开发了可扩展的边界链接算法BLADE，该算法通过使用基于分数的直接目标批次和热启动Katz更新，避免了密集Katz内核维护。在合成和真实网络上的实验表明，BLADE使用比自然基线少得多的编辑达到了所需的Top-k表示，同时可扩展到大型真实图并保留原始排名结构。
英文摘要
Centrality measures are widely used to rank nodes in networked data, but fairness interventions for graph centrality typically target global score mass or modify the centrality operator rather than controlling who appears in the displayed top-k ranking. We study this top-k setting for Katz centrality. Given a target group proportion, an admissible set of directed edge additions, and a fairness tolerance, the goal is to find the smallest edit set whose resulting Katz top-k ranking satisfies the target representation constraint. We formalize this problem as Fair Top-k Katz Centrality Design and show that the minimum-edit objective is strongly inapproximable, ruling out worst-case polynomial-time approximation guarantees unless P = NP. We then derive closed-form Katz sensitivity expressions showing that useful edits are boundary-driven: they must help promotable nodes outside the top-k set overtake opposing nodes inside it. Based on this structure, we develop BLADE, a scalable boundary-link algorithm that avoids dense Katz-kernel maintenance by using score-based direct-target batches and warm-started Katz updates. Experiments on synthetic and real-world networks show that BLADE reaches the desired top-k representation using far fewer edits than natural baselines, while scaling to large real-world graphs and preserving the original ranking structure.
