高阶连接的相关性
The relevance of higher-order ties
AI总结：
本文提出阶数贡献、阶数相关性和标签组平衡三种度量，量化不同规模超链接对网络结构的贡献及其协同或冗余关系，并在董事会连锁网络和科学合作网络中发现前者呈协同贡献、后者更多冗余。
摘要：
高阶网络能够有效表示具有群体交互的复杂系统。现有方法通常忽略了不同规模的群体交互（超链接）对整体网络结构的相对贡献。然而，这具有许多重要应用，尤其是在网络具有有意义的节点标签时。在这项工作中，我们提出了一套综合方法来精确衡量不同阶数对整体网络结构的贡献。首先，我们提出了阶数贡献度量，用于量化不同阶数的超链接对成对加权网络的链接权重（局部尺度）、三角形数量（中尺度）和最大连通分量规模（全局尺度）的贡献。其次，我们提出了阶数相关性度量，该度量揭示了不同阶数的超链接如何对所考虑的网络属性做出贡献。最有趣的是，它能够评估这种贡献相对于其他阶数超链接的贡献是协同的还是冗余的。第三，为了考虑标签，我们提出了标签组平衡度量，以评估不同阶数的超链接如何连接由标签诱导的节点组。我们将这些度量应用于大规模董事会连锁网络和科学合作网络，其中节点标签对应于节点的地理位置。包括与随机零模型比较在内的实验揭示了从全局层面视角来看，我们在董事会连锁网络中观察到各阶数的协同贡献，而在合作网络中存在更多冗余。这些发现为社会科学的争论提供了新的视角，涉及忙碌董事在全球商业网络中的作用以及大型作者团队在科学合作网络中的连接效应。
英文摘要：
Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperlinks) of different sizes to the overall network structure. Yet, this has many important applications, especially when the network has meaningful node labels. In this work, we propose a comprehensive methodology to precisely measure the contribution of different orders to the overall network structure. First, we propose the order contribution measure, which quantifies the contribution of hyperlinks of different orders to the link weights (local scale), number of triangles (mesoscale) and size of the largest connected component (global scale) of the pairwise weighted network. Second, we propose the measure of order relevance, which gives insights in how hyperlinks of different orders contribute to the considered network property. Most interestingly, it enables an assessment of whether this contribution is synergistic or redundant with respect to that of hyperlinks of other orders. Third, to account for labels, we propose a metric of label group balance to assess how hyperlinks of different orders connect label-induced groups of nodes. We applied these metrics to a large-scale board interlock network and scientific collaboration network, in which node labels correspond to geographical location of the nodes. Experiments including a comparison with randomized null models reveal how from the global level perspective, we observe synergistic contributions of orders in the board interlock network, whereas in the collaboration network there is more redundancy. The findings shed new light on social scientific debates on the role of busy directors in global business networks and the connective effects of large author teams in scientific collaboration networks.
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