We uncover a new relation between Closeness centrality and the Condorcet principle. We define a Condorcet winner in a graph as a node that compared to any other node is closer to more nodes. In other words, if we assume that nodes vote on a closer candidate, a Condorcet winner would win a two-candidate election against any other node in a plurality vote. We show that Closeness centrality and its random-walk version, Random-Walk Closeness centrality, are the only classic centrality measures that are Condorcet consistent on trees, i.e., if a Condorcet winner exists, they rank it first. While they are not Condorcet consistent in general graphs, we show that Closeness centrality satisfies the Condorcet Comparison property that states that out of two adjacent nodes, the one preferred by more nodes has higher centrality. We show that Closeness centrality is the only regular distance-based centrality with such a property.
翻译：我们发现了“近距离中心”和“神鹰”原则之间的新关系。 我们在图表中将“神鹰”获胜者定义为“节点”,与任何其他节点相比,它比其他节点更接近。换句话说,如果我们假设对更接近的候选人有节点票,那么“神鹰”获胜者将赢得“双向”选举,在多元投票中将赢得“近距离中心”和“其他节点”之间的新关系。我们显示,“近距离中心”和“随机行”版本“随机方向中心”是唯一在树上一致的典型核心措施,即,如果“神鹰”获胜者存在,它们首先排在节点上排位。虽然在一般图表中它们不是“神鹰”一致,但我们表明,“神鹰”中心满足了“神鹰”比较属性,在两个相邻的节点中,被更多节点所偏爱的节点具有更高的中心地位。我们显示,“近距离中心”是唯一在树上以距离为基础的常规中心。
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