Fig. 12.

The selected graph in anatomical space and functional space: This figure shows the graph selected (on the basis of the posterior probabilities in the previous figure) in anatomical space and functional (spectral embedding) space. The upper panel shows the same regions depicted in Fig. 9, but now connected using the conditional means of the coupling parameters, under the model selected. The colour of the arrow reports the source of the strongest bidirectional connection, while its width represents its absolute (positive or negative) strength. This provides a description of the architecture or graph in anatomical space. A more functionally intuitive depiction of this graph is provided in the lower panel. Here, we have used spectral embedding to place the nodes in a functional space, where the distance between them reflects the strength of bidirectional coupling. Spectral embedding uses the eigenvectors vectors (principle components) of the weighted graph Laplacian to define a small number of dimensions that best capture the proximity or conditional dependence between nodes. Here, we have used the first three eigenvectors to define this functional space. The weighted adjacency matrix was, in this case, simply the maximum (absolute) conditional estimate of the coupling parameters described in the previous figure. The middle panel shows the asymmetry strengths based on the conditional estimates of the selected model. This provides a further way of characterising the functional architecture in hierarchical terms, based on (bidirectional) coupling.