Closure Coefficient in Complex Directed Networks.

The 3-clique formation, a natural phenomenon in real-world networks, is typically measured by the local clustering coefficient, where the focal node serves as the centre-node in an open triad. The local closure coefficient provides a novel perspective, with the focal node serving as the end-node. It has shown some interesting properties in network analysis, yet it cannot be applied to complex directed networks. Here, we propose the directed closure coefficient as an extension of the closure coefficient in directed networks, and we extend it to weighted and signed networks. In order to better use it in network analysis, we introduce further the source closure coefficient and the target closure coefficient. Our experiments show that the proposed directed closure coefficient provides complementary information to the classic directed clustering coefficient. We also demonstrate that adding closure coefficients leads to better performance in link prediction task in most directed networks.