Graph-matching distance between individuals' functional connectomes varies with relatedness, age, and cognitive score

Functional connectomes (FCs), represented by networks or graphs that summarize coactivation patterns between pairs of brain regions, have been related at a population level to age, sex, cognitive/behavioral scores, life experience, genetics, and disease/disorders. However, quantifying FC differences between individuals also provides a rich source of information with which to map to differences in those individuals' biology, experience, genetics or behavior. In this study, graph matching is used to create a novel inter-individual FC metric, called swap distance, that quantifies the distance between pairs of individuals' partial FCs, with a smaller swap distance indicating the individuals have more similar FC. We apply graph matching to align FCs between individuals from the the Human Connectome Project $\left(N=997\right)$ and find that swap distance (i) increases with increasing familial distance, (ii) increases with subjects' ages, (iii) is smaller for pairs of females compared to pairs of males, and (iv) is larger for females with lower cognitive scores compared to females with larger cognitive scores. Regions that contributed most to individuals' swap distances were in higher-order networks, that is, default-mode and fronto-parietal, that underlie executive function and memory. These higher-order networks' regions also had swap frequencies that varied monotonically with familial relatedness of the individuals in question. We posit that the proposed graph matching technique provides a novel way to study inter-subject differences in FC and enables quantification of how FC may vary with age, relatedness, sex, and behavior.