  Research into binary network analysis of brain function faces a
methodological challenge in selecting an appropriate threshold to binarise edge
weights. For EEG phase-based functional connectivity, we test the hypothesis
that such binarisation should take into account the complex hierarchical
structure found in functional connectivity. We explore the density range
suitable for such structure and provide a comparison of state-of-the-art
binarisation techniques, the recently proposed Cluster-Span Threshold (CST),
minimum spanning trees, efficiency-cost optimisation and union of shortest path
graphs, with arbitrary proportional thresholds and weighted networks. We test
these techniques on weighted complex hierarchy models by contrasting model
realisations with small parametric differences. We also test the robustness of
these techniques to random and targeted topological attacks.We find that the
CST performs consistenty well in state-of-the-art modelling of EEG network
topology, robustness to topological network attacks, and in three real
datasets, agreeing with our hypothesis of hierarchical complexity. This
provides interesting new evidence into the relevance of considering a large
number of edges in EEG functional connectivity research to provide
informational density in the topology.
