ABSTRACT

Despite a plethora of centrality measures were proposed, there is no consensus on what centrality is exactly due to the shortcomings each measure has. In this manuscript, we propose to combine centrality measures pertinent to a network by forming their convex combinations. We found that some combinations, induced by regular points, split the nodes into the largest number of classes by their rankings. Moreover, regular points are found with probability $1$ and their induced rankings are insensitive to small variation. By contrast, combinations induced by critical points are scarce, but their presence enables the variation in node rankings. We also discuss how optimum combinations could be chosen, while proving various properties of the convex combinations of centrality measures.

摘要

尽管提出了过多的中心性度量，但由于每个度量都存在缺陷，因此对于中心性究竟是什么还没有达成共识。在这篇手稿中，我们建议通过形成凸组合来结合与网络相关的中心性度量。我们发现一些由规则点引起的组合，根据节点的排名将节点分成最多的类。此外，以概率找到规则点$1$并且它们的诱导排名对小的变化不敏感。相比之下，由临界点引起的组合很少，但它们的存在使节点排名发生变化。我们还讨论了如何选择最佳组合，同时证明中心性度量的凸组合的各种属性。