Efficient small-world and scale-free functional brain networks at rest using k-nearest neighbors thresholding

In recent years, there has been a massive effort to analyze the topological properties of brain networks. Yet, one of the challenging questions in the field is how to construct brain networks based on the connectivity values derived from neuroimaging methods. From a theoretical point of view, it is plausible that the brain would have evolved to minimize energetic costs of information processing, and therefore, maximizes efficiency as well as to redirect its function in an adaptive fashion, that is, resilience. A brain network with such features, when characterized using graph analysis, would present small-world and scale-free properties. In this paper, we focused on how the brain network is constructed by introducing and testing an alternative method: k-nearest neighbor (kNN). In addition, we compared the kNN method with one of the most common methods in neuroscience: namely the density threshold. We performed our analyses on functional connectivity matrices derived from resting state fMRI of a big imaging cohort (N=434) of young and older healthy participants. The topology of networks was characterized by the graph measures degree, characteristic path length, clustering coefficient and small world. In addition, we verified whether kNN produces scale-free networks. We showed that networks built by kNN presented advantages over traditional thresholding methods, namely greater values for small-world (linked to efficiency of networks) than those derived by means of density thresholds and moreover, it presented also scale-free properties (linked to the resilience of networks), where density threshold did not. A brain network with such properties would have advantages in terms of efficiency, rapid adaptive reconfiguration and resilience, features of brain networks that are relevant for plasticity and cognition as well as neurological diseases as stroke and dementia.