The Complex Hierarchical Topology of EEG Functional Connectivity

TL;DR

This paper introduces new metrics and models to analyze the hierarchical complexity of EEG brain networks, revealing a broader and more nuanced understanding of their topological features than previous methods.

Contribution

The authors develop a novel metric and the Weighted Complex Hierarchy (WCH) model to better characterize hierarchical complexity in weighted brain networks.

Findings

Highest complexity occurs between random and class-based topologies.

WCH model matches EEG phase-lag network complexity at peak performance.

New metric captures greater differences in network complexity than previous metrics.

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.