Evaluating structural symmetry of weighted brain networks via graph matching.

We study the symmetry of weighted brain networks to understand the roles of individual brain areas and the redundancy of the brain connectivity. We quantify the structural symmetry of every node pair in the network by isomorphism of the residual graphs of those nodes. The efficacy of the symmetry measure is evaluated on both simulated networks and real data sets. In the resting state fMRI (rs-fMRI) data, we discover that subjects with inattentive type of Attention Deficit Hyperactivity Disorder (ADHD) demonstrate a higher level of network symmetry in contrast to the typically development group, consistent with former findings. Moreover, by comparing the average functional networks of normal subjects during resting state and activation, we obtain a higher symmetry level in the rs-fMRI network when applying median thresholds to the networks. But the symmetry levels of the networks are almost the same when larger thresholds are used, which may imply the invariance of the prominent network symmetry for ordinary people.