Figure 1
Global Granger causality approach. (A) Ancestors of target node T, A0(T) = {T1, T2, T3, X1,...,Xn, Y1,...,Yn}. T1, T2, T3 are direct ancestors to target T. {X1,...,Xn} connect to T through a single pathway, thus, {X1,...,Xn} are not direct ancestors to target T. {Y1,...,Yn} connect to T through two distinctive pathways (B) {X1,...,Xn} can be removed by Granger-conditioning on a single node, A1(T) = { T1,T2,T3,Y1,...,Yn}. (C) S is connected to T through two different paths, both {B1,B2} and {B3} are sections from S to T, but {B3} is the bottleneck. (D) There may exist other common drives to the observed nodes X and T, we assume the partial Granger causality can delete the influence of such drive and exclude such case in our analysis. (E) Histograms of the number of bottleneck for a variety of connection probability p for N = 100 and 500 simulations.