A Framework for the Evaluation of Complete Weighted Network Topology in EEG Functional Connectivity

Background: Graph theory provides an analytical framework for brain functional connectivity. The complete weighted networks (CWNs) derived from functional connectivity analyses are fundamentally different to the sparse binary networks studied in other research areas. Nonetheless, CWNs are typically analysed using sparse network methodology. New Methods: We offer an alternative framework for brain networks designed specifically for CWN analysis, generalising widely used binary network models to CWN form and analysing at different densities using straightforward metrics related to the main topological features of brain networks: integration, regularity and modularity. Importantly, we introduce two novel techniques which complement and enhance this framework. Firstly, a new metric to measure the complexity of a network. Secondly, a new CWN null model for EEG functional connectivity. Results: Our complexity metric is demonstrated to be a specific classifier for real world network behaviour. Our null model offers an unprecedented ease and rigour of comparability for functional brain networks exactly because of its CWN formulation. Demonstrating these techniques in the context of EEG networks obtained from both zero-lag and phase-lag connectivity measures, we reveal that EEG phase-lag networks attain the maximal values of complexity achieved by our CWN null model. Comparison to existing methods: This framework extends existing methodology and is not directly comparable to other methods. Particularly, our null model is the first CWN null model. Complexity shows important differences to the three pre-existing topological features. Conclusions: These developments offer solid and flexible foundations for research in functional connectivity, but also, more generally, the implications extend to all graph analysis domains.