title: The complex hierarchical topology of EEG functional connectivity.
abstract: Understanding 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.
  
  
  
  We 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.
  
  
  
  By 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.
  
  
  
  Hierarchical 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.
  
  
  
  Our 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.
authors.affiliation: Institute for Digital Communications, School of Engineering, University of Edinburgh, West Mains Rd, Edinburgh EH9 3FB, UK; Alzheimer Scotland Dementia Research Centre, University of Edinburgh, 7 George Square, Edinburgh EH8 9JZ, UK. Electronic address: k.smith@ed.ac.uk.
authors.forename: Keith
authors.initials: K
authors.lastname: Smith
authors.affiliation: Institute for Digital Communications, School of Engineering, University of Edinburgh, West Mains Rd, Edinburgh EH9 3FB, UK. Electronic address: javier.escudero@ed.ac.uk.
authors.forename: Javier
authors.initials: J
authors.lastname: Escudero
mesh_terms: D001921:Brain / Q000502:physiology*; D004569:Electroencephalography / Q000379:methods; D006801:Humans; D008962:Models, Theoretical; D009434:Neural Pathways / Q000502:physiology
keywords: Brain networks; Electroencephalogram; Functional connectivity; Hierarchical complexity; Network simulation