Figure 1
(A) A schematic representation of a brain multiplex network, where the networks of functional connectivity (FC) and structural connectivity (SC) are coupled via one-to-one match between corresponding region of interests; hub nodes in the SC (denoted as bigger circles) may not coincide with high-degree nodes in the FC; nodes linked in SC may not co-activate strongly, resulting in the absence of the edge in FC. (B) Limitations of Pearson’s correlation and partial correlation. Depending on the underlying neuronal circuits both approaches can result in undesirable connection weights in the functional graph. (Left) A case where Pearson’s correlation coefficient fails to disregard a non-existent connection between node A and C. The visualization stands for the underlying probabilistic graphical model among the variables A, B, and C, with connections standing for dependencies among pairs of variables. The two matrices contain the coefficients of Pearson’s correlation and partial correlation coefficients, respectively. Rows and columns of the matrices refer to alphabetically ordered pairs of variable. Given their symmetry, we show only the upper-triangle of the matrices. (Right) A case where the partial correlation coefficient counter-intuitively imposes a high weight on the connection between node A and B due to the dependence on C. (Adapted from Nie 201581).
