Evaluating the reliability, validity, and utility of overlapping networks: Implications for network theories of cognition

Brain network definitions typically assume nonoverlap or minimal overlap, ignoring regions' connections to multiple networks. However, new methods are emerging that emphasize network overlap. Here, we investigated the reliability and validity of one assignment method, the mixed membership algorithm, and explored its potential utility for identifying gaps in existing network models of cognition. We first assessed between‐sample reliability of overlapping assignments with a split‐half design; a bootstrapped Dice similarity analysis demonstrated good agreement between the networks from the two subgroups. Next, we assessed whether overlapping networks captured expected nonoverlapping topographies; overlapping networks captured portions of one to three nonoverlapping topographies, which aligned with canonical network definitions. Following this, a relative entropy analysis showed that a majority of regions participated in more than one network, as is seen biologically, and many regions did not show preferential connection to any one network. Finally, we explored overlapping network membership in regions of the dual‐networks model of cognitive control, showing that almost every region was a member of multiple networks. Thus, the mixed membership algorithm produces consistent and biologically plausible networks, which presumably will allow for the development of more complete network models of cognition.