Figure 4. .

Edges can report both anatomical and functional relationships between regions. (A) How these two topologies relate to each other remains an important topic of investigation for network neuroscience; one way to approach this question is to model how communication processes, guided by certain algorithmic rules, might unfold over the structural edges. In shortest paths routing, communication between a source and target node unfolds along the shortest structural path. From the perspective of a diffusion process or knowledgeless random walker, accessing the shortest path may be difficult if there exist opportunities for the walker to “hop” off the path (we show these opportunities as black arrows in the middle panel). The total information (usually expressed in units of bits) required to navigate the shortest path successfully is referred to as “search information.” Even if a random walker diverges from the shortest path, there may be opportunities to return. This intuition is quantified by the measure “path transitivity,” which identifies cases where, following deviations from a network’s shortest path, a random walker can return. In the figure, we highlight three such cases, plotting the deviation and return as a filled triangle (red, black, and green). (B) The mapping between structure and function can also be estimated via deep learning, which can achieve high prediction accuracies at the group and individual levels (Sarwar, Tian, Yeo, Ramamohanarao, & Zalesky, 2021). Although such an approach cannot uncover putative neurophysiological mechanisms, the model performance can serve as a benchmark for other types of structure-function mapping models (figure adapted from Sarwar et al., 2021).