School of Computer Science, University of Technology Sydney, Sydney, NSW, Australia.
PLoS One. 2021 Jun 25;16(6):e0253822. doi: 10.1371/journal.pone.0253822. eCollection 2021.
The triangle structure, being a fundamental and significant element, underlies many theories and techniques in studying complex networks. The formation of triangles is typically measured by the clustering coefficient, in which the focal node is the centre-node in an open triad. In contrast, the recently proposed closure coefficient measures triangle formation from an end-node perspective and has been proven to be a useful feature in network analysis. Here, we extend it by proposing the directed closure coefficient that measures the formation of directed triangles. By distinguishing the direction of the closing edge in building triangles, we further introduce the source closure coefficient and the target closure coefficient. Then, by categorising particular types of directed triangles (e.g., head-of-path), we propose four closure patterns. Through multiple experiments on 24 directed networks from six domains, we demonstrate that at network-level, the four closure patterns are distinctive features in classifying network types, while at node-level, adding the source and target closure coefficients leads to significant improvement in link prediction task in most types of directed networks.
三角形结构作为一个基本且重要的元素，是研究复杂网络的许多理论和技术的基础。三角形的形成通常通过聚类系数来衡量，其中焦点节点是开放三元组中的中心节点。相比之下，最近提出的闭包系数从末端节点的角度来衡量三角形的形成，已被证明是网络分析中的一个有用特征。在这里，我们通过提出有向闭包系数对其进行扩展，以衡量有向三角形的形成。通过在构建三角形时区分闭合边的方向，我们进一步引入源闭包系数和目标闭包系数。然后，通过对特定类型的有向三角形（例如，路径头）进行分类，我们提出了四种闭包模式。通过在六个领域的 24 个有向网络上进行多项实验，我们证明，在网络层面，这四种闭包模式是区分网络类型的独特特征，而在节点层面，在大多数类型的有向网络中，添加源和目标闭包系数可以显著提高链路预测任务的性能。
