Applied Mathematics Correction for “Indirect influence in social networks as an induced percolation phenomenon,” by Jiarong Xie, Xiangrong Wang, Ling Feng, Jin-Hua Zhao, Wenyuan Liu, Yamir Moreno, and Yanqing Hu, which published February 25, 2022; 10.1073/pnas.2100151119 (Proc. Natl. Acad. Sci. U.S.A. 119, e2100151119).
The authors note that Fig. 2 appeared incorrectly. An arrow in Fig. 2 B and C was misplaced. The corrected figure and its legend appear below. The online version has been corrected.
Fig. 2.
Induced percolation on directed networks. A illustrates the proposed mechanism of induced percolation for the case m = 2. In order for a node i to remain in state 1, at least one node (j) at the other end of an incoming link should be in state 1. In its turn, j should also have at least m ( in the example) incoming links from neighbors that are in state 1. B shows a directed graph of eight nodes all in state 1. C shows the GOUT at equilibrium state when the graph on panel B is pruned according to the induced percolation rules. D and E illustrate the variables x and y defined in the main text by Eqs. 3 and 4. F and G show the relationship between the order parameters GSCC, GIN, and GOUT for induced percolation and typical bond percolation processes, respectively. H schematically represents the multilayer representation employed to derive the order parameter P∞ when there are directed and undirected links in the substrate network.