Brain Network Measures for Groups of Nodes: Application to Normal Aging and Alzheimer's Disease.

The nodal brain network measures (e.g., centrality measures) are defined for a single node and the global network measures (e.g., global efficiency) are defined for the whole brain in the literature. But a meaningful group of nodes will be benefited from a formulation that applies to a group of nodes rather than a single node or the whole brain. The question such as "which brain lobe is more structurally central in the older-adult brain?" could be answered to some extent by the application of a centrality measure that applied to the group of nodes from each lobe. In the brain asymmetric studies, path-based global measures were applied to the left and right hemispherical networks separately, considering only intrahemispheric edges. However, for a valid comparison, such global measures should include the interhemispheric edges as well. This problem can be solved by considering both hemispherical nodes as two groups in one network. Novel definitions for group nodes network measures are presented in this study, to solve a number of such group-context problems in the brain networks analysis. We apply the group measures to the structural connectomes of older adults and Alzheimer's disease (AD) subjects based on the brain lobes and hemispherical groups to demonstrate the effectiveness of the proposed measures. The temporal and parietal lobes are the most central lobes in older adults and AD, but the strength of these lobes has been heavily affected in AD. However, the rewiring of the AD brain preserves the paths for communication between other regions through these lobes. Leftward efficiency revealed in older adults and the asymmetry disappeared in the rewired AD. We prove that the concepts of group network measures have the potential to solve a number of such group-context problems in the brain networks analysis and the group network measures change the way of analyzing brain networks.