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Percolation theory has been widely used to study phase transitions in network systems. It has also successfully explained various macroscopic spreading phenomena across different fields. Yet, the theoretical frameworks have been focusing on direct interactions among nodes, while recent empirical observations have shown that indirect interactions are common in many network systems like social and ecological networks, among others. By investigating the detailed mechanism of both direct and indirect influence on scientific collaboration networks, here we show that indirect influence can play the dominant role in behavioral influence. To address the lack of theoretical understanding of such indirect influence on the macroscopic behavior of the system, we propose a percolation mechanism of indirect interactions called induced percolation. Surprisingly, our model exhibits a unique anisotropy property. Specifically, directed networks show first-order abrupt transitions as opposed to the second-order continuous transition in the same network structure but with undirected links. A mix of directed and undirected links leads to rich hybrid phase transitions. Furthermore, a unique feature of the nonmonotonic pattern is observed in network connectivities near the critical point. We also present an analytical framework to characterize the proposed induced percolation, paving the way to further understanding network dynamics with indirect interactions. Published version This work is supported by the Guangdong High-Level Personnel of Special Support Program, Young TopNotch Talents in Technological Innovation (grant no. 2019TQ05X138), Natural Science Foundation of Guangdong for Distinguished Youth Scholar, Guangdong Provincial Department of Science and Technology (grant no. 2020B1515020052), the National Natural Science Foundation of China (grant nos. 61903385 and 62003156), Guangdong Major Project of Basic and Applied Basic Research (grant no. 2020B0301030008), and the Chinese Academy of Sciences (grant no. QYZDJSSW-SYS018). |
