标题： 网络排名中的少数群体代表性：估计、检验和公平性的方法 显示英文标题

标题： Minority Representation in Network Rankings: Methods for Estimation, Testing, and Fairness

摘要： 网络由节点及其连接组成，在各个领域中被广泛用于建模复杂的关系。中心性度量通常用于决策，例如识别关键节点或优先分配资源。然而，网络经常存在缺失或错误的边，这可能会系统性地影响基于中心性的决策，并扭曲某些受保护群体的表示。为了解决这个问题，我们引入了少数群体代表性的正式定义，即在排名靠前的节点中少数群体节点的比例。我们通过使用与群体相关的缺失边错误来建模对少数群体的系统性偏差。我们提出了估计和检测系统性偏差的方法。在典型的网络模型下推导了少数群体代表性统计量的渐近极限，并用于校正节点排名中的少数群体表示。模拟结果证明了我们估计、检验和排名校正程序的有效性，并我们将这些方法应用于一个接触网络，展示了它们的实际适用性。 显示英文摘要

摘要： Networks, composed of nodes and their connections, are widely used to model complex relationships across various fields. Centrality metrics often inform decisions such as identifying key nodes or prioritizing resources. However, networks frequently suffer from missing or incorrect edges, which can systematically centrality-based decisions and distort the representation of certain protected groups. To address this issue, we introduce a formal definition of minority representation, measured as the proportion of minority nodes among the top-ranked nodes. We model systematic bias against minority groups by using group-dependent missing edge errors. We propose methods to estimate and detect systematic bias. Asymptotic limits of minority representation statistics are derived under canonical network models and used to correct representation of minority groups in node rankings. Simulation results demonstrate the effectiveness of our estimation, testing, and ranking correction procedures, and we apply our methods to a contact network, showcasing their practical applicability.