The complex hierarchical topology of EEG functional connectivity

- A novel framework for functional connectivity networks is presented.
- A metric to analyse the hierarchical complexity of networks is introduced.
- A functional connectivity null model for complete weighted networks is introduced.
- The null model attains highest complexity when mimicking EEG phase-lag networks.
- Key network concepts - integration, regularity, topological randomness - are refined.

BackgroundUnderstanding the complex hierarchical topology of functional brain networks is a key aspect of functional connectivity research. Such topics are obscured by the widespread use of sparse binary network models which are fundamentally different to the complete weighted networks derived from functional connectivity.New methodsWe introduce two techniques to probe the hierarchical complexity of topologies. Firstly, a new metric to measure hierarchical complexity; secondly, a Weighted Complex Hierarchy (WCH) model. To thoroughly evaluate our techniques, we generalise sparse binary network archetypes to weighted forms and explore the main topological features of brain networks - integration, regularity and modularity - using curves over density.ResultsBy controlling the parameters of our model, the highest complexity is found to arise between a random topology and a strict 'class-based' topology. Further, the model has equivalent complexity to EEG phase-lag networks at peak performance.Comparison to existing methodsHierarchical complexity attains greater magnitude and range of differences between different networks than the previous commonly used complexity metric and our WCH model offers a much broader range of network topology than the standard scale-free and small-world models at a full range of densities.ConclusionsOur metric and model provide a rigorous characterisation of hierarchical complexity. Importantly, our framework shows a scale of complexity arising between 'all nodes are equal' topologies at one extreme and 'strict class-based' topologies at the other.

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